tl;dr: There are at least 6, up to 9 depending how you count:
- 1x03 "Lord Snow"
- 2x08 "The Prince of Winterfell"
- 3x01 "Valar Dohaeris"
- 3x02 "Dark Wings, Dark Words"
- 3x07 "The Bear and the Maiden Fair"
- 8x02 "A Knight of the Seven Kingdoms"
- 6x07 "The Broken Man" (nothing fitting my arbitrary rules below, see description further on.)
- 6x05 "The Door" (see below).
- 6x06 "The Blood of my Blood"
Let's take the more through route and find out via process of elimination, preferably with some named (though maybe only in the books) character. I'll be extra fun and give the timestamp (for HBO GO) for the first death that fits the rules below.
Because you're asking about deaths, assume everything is a spoiler herein.
The question title makes this clear anyways...
- a corpse is shown: ignored
- a Raven says someone died: ignored
- during a time jump: ignored
- generic screaming in the background during a big fight: ignored
- screaming, screaming, silence by a distinct person: counts
I start timing from the HBO "static" logo (subtracting commercials and "Previously on...").
- "Winter Is Coming"
6:58 Gared beheaded by a White Walker.
- "The Kingsroad"
31:30 Would-be assassin mauled by Summer (these sorts of death would be from hypovolemic shock).
- "Cripples, Bastards, and Broken Things"
47:55 Ser Hugh lanced through the neck (presumed gorget failure) by the Mountain.
- "The Wolf and the Lion"
12:07 Bronn slices a tribesman's neck open.
- "A Golden Crown"
11:23 Robb slices a wildling's neck open.
- "You Win or You Die"
56:26 A goldcloak pierces a Stark footman through the chest (death by shock).
- "The Pointy End"
2:07 (Only 15 seconds past intro animation) a Lannister footman slices a Stark man's neck.
34:05 Ser Jorah slices Qotho across the face.
- "Fire and Blood"
49:15 Mirri Maz Duur burned alive (asphyxiation).
- "The North Remembers"
2:09 A blow from The Hound sends a combatant off a ledge.
- "The Night Lands"
(The head of Rakharo is seen, but this death didn't really occur on screen, a sacrifice is also offered to the Walkers).
- "What Is Dead May Never Die"
48:00 Yoren slices a Lannister arbalist that shot him across the neck.
- "Garden of Bones"
20:45 Prisoner killed via torture device (likely cervical dislocation).
- "The Ghost of Harrenhal"
3:45 A shadowy figure stabs Renly Baratheon through the heart.
- "The Old Gods and the New"
9:40 Theon Greyjoy bludgeons Ser Rodrik's neck with a sword.
- "A Man Without Honor"
38:53 Jaime Lannister bashes Alton Lannister's head in using his shackles.
"The Price of Winterfell"
Qhorin alludes to his companions (Stonesnake, et al.) dying. There are a couple dozen dead bodies shown around Harrenhal, hung by the neck or pinned to a wall (e.g. those Jaquen H'ghar dispatched), but no one actually killed on screen.
25:10 Bronn ignites the wildfire-laden ship. Probably kills a lot of people right then, as it disintegrates Davos's ship with little effort, but about a minute later you see a flaming sailor abruptly go silent.
- "Valar Morghulis"
15:39 Brienne cuts a Stark footman short after he asks too many questions.
2:10 Ser Jeor Mormont torches a wight. They're already dead perhaps, so doesn't count. Again, like with "The Prince of Winterfell" you see scores of dead bodies when Robb gets to Harrenhal, but no living people turning into dead people.
"Dark Wings, Dark Words"
Nothing on-screen. News of Catlyn’s father, Hoster Tully, passing comes here.
- "Walk of Punishment"
44:38 Ramsy Snow snipes several men.
- "And Now His Watch Is Ended"
38:49 Karl spikes Craster up through the bottom of his head with a dagger.
- "Kissed by Fire"
4:45 Sandor Clegane temporarily kills Beric Dondarrion. For something more final, 25:28 Robb executes Rickard Karstark.
- "The Climb"
38:12 The wall defends itself, killing a few wildlings.
"The Bear and the Maiden Fair"
The bear almost gets the maiden fair, but nothing comes of it.
- "Second Sons"
54:28 Sam stabs a White Walker. If you don’t count the undead dying, then all you really see are two heads from a duffel bag, so no deaths.
- "The Rains of Castamere"
25:03 Ygrette feathers the horse farmer.
2:25 A Frey man beheads a Stark man on a barrel.
- "Two Swords"
55:06 After the Hound knocks Polliver's gang around, finally kills one by jamming his head down onto a knife repeatedly.
- "The Lion and the Rose"
4:05 Ramsey Snow's hounds savage Tansy after hunting her for sport.
- "Breaker of Chains"
4:35 Petyr Balish's men dispatch Dontos Hollard after he delivers Sansa.
7:50 A crush of slaves mob a Master.
- "First of His Name"
43:00 The Night's Watch task force led by Jon Snow assaults the traitors at Craster’s Keep.
- "The Laws of Gods and Men"
11:41 Yara Greyjoy plants an axe in the forehead of a Dreadfort watchman.
4:55 The Mountain practices on some prisoners.
- "The Mountain and the Viper"
4:25 A Thenn kills a thirsty man.
- "The Watchers on the Wall"
22:15 Night's Watch archers bury some arrows in wildlings as they charge Castle Black.
- "The Children"
9:10 One of Stannis's cavalrymen lances a Mance man.
- "The Wars to Come"
15:22 An Unsullied gets his throat cut in a brothel.
- "The House of Black and White"
13:43 A bodyguard of Littlefinger sprouts a sword out the back of his neck (Brienne slashed one at at 11:30; but it seemed like a lazy cut across some armor).
- "High Sparrow"
2:55 A man gives himself as an offering to the Many-Faced God.
- "Sons of the Harpy"
34:32 Another vascular neck injury, this time caused by Bronn.
- "Kill the Boy"
5:24 Dany feeds her children some long pig, well-done.
- "Unbowed, Unbent, Unbroken"
13:32 Arya gives a man's terminally-ill daughter the gift.
- "The Gift"
9:45 Maester Aemon Targaryen dies... way too peaceful and out-of-character for this show. And despite a hard cut from him being alive to dead, not technically on-screen?... Doesn't count.
46:44 A free man fighting in the slave pits gets shivved in the neck. That's better.
32:54 Tormund disagrees with the Lord of Bones.
- "The Dance of Dragons"
24:49 A man visits the House of Black and White seeking the gift. (33:57 for involuntary human sacrifice).
- "Mother's Mercy"
13:44 Coup de grâce to a Stannis man.
- "The Red Woman"
16:22 Brienne opens a Bolton's neck.
9:33 Wun Weg Wun Dar Wun obliterates an archer that shot him in the back (Tormund gets a guy 15 seconds earlier in the scene, but this one is far better).
14:10 Ser Gerold Hightower runs a Stark man through.
49:26 for something in the present-tense: the Lord-Commander of the Night's Watch executes mutineers.
- "Book of the Stranger"
24:23 Dario twists the neck of a Dothraki.
- "The Door"
17:00 the reason for the Night's Watch is born. For something in the present tense, a Child of the Forest dies (49:47) and the Three-Eyed Raven (51:55). The first is a supernatural transformation, the later ones are supernatural characters, and the episode's namesake is not definitively dead, so if you're super picky, maaaaybe this one.
"Blood of My Blood"
Three-Eyed Raven montages with some violence, Coldhands kills some wights at the start, and no-one almost poisons a lady, but nothing else.
- "The Broken Man"
Nothing technically on-screen, but 47:43 has screams from the faithful followed by the gruesome aftermath.
- "No One"
8:46 The Hound starts his revenge for the above.
- "The Battle of the Bastards"
7:31 A Son of the Harpy slices open someone's throat.
- "The Winds of Winter"
13:10 The coup begins with Pycelle getting pecked to death by little birds.
3:00 Arya poisons a room full of Freys.
50:48 A guy gets flattened by Euron's corvus.
- "The Queen's Justice"
Kiss of death with "The Long Farewell" at 26:20, but for something more acute, at 51:30 Unsullied falls off a ladder, among others.
- "The Spoils of War"
38:40 Drogon makes some Lannister BBQ
9:12 Drogon makes some Tarly BBQ
- "Beyond the Wall"
22:43 Bear with blue eyes kills a red shirt.
- "The Dragon and the Wolf"
22:10 A wight dies again.
52:02 Theon gets his balls back. Was just a fist-fight, so probably just unconscious.
58:34 Littlefinger falls off the ladder of chaos, reaching the pinnacle of stability.
25:15 arrows sprout out of some Ironborn.
"A Knight of the Seven Kingdoms"
remembrances before the battle.
- "The Long Night"
12:30 lights start going out in the dark
15:40 Unsullied start to get up close and personal with the literal wave of death.
- "The Last of the Starks"
Opens on the dead from the previous episode...
52:30 Rhaegal meets the drowned god, but not a human...
1:14:45 Missandei is executed.
- "The Bells"
12:08 Varys meets Dracarys
- "The Iron Throne"
6:26 Gray Worm executes a Lannister prisoner
33:22 (bonus!) last death of the series, btw.