The Doctor doesn't seem to mind killing Daleks and various other things, but is also very concerned about saving lives.
Daleks and many other "baddies" are sentient beings. The Doctor has hesitated in the past, such as when they declined to destroy the Dalek race before it could become a threat.
Has The Doctor ever explained or demonstrated a code or logic as to what killing is acceptable and what isn't?
I think it depends on which Doctor you are talking about.
For example, the ninth Doctor is much more likely to kill at the first sight of trouble. In particular, letting Cassandra die, torturing the dalek, killing the Mighty Jagrafess wanting to send Blon Fel-Fotch Passameer-Day Slitheen to her execution etc. However, by the ninth Doctor’s conclusion he picks being a coward over killer, paving the way for his perspective on killing to change.
This change is seen in the 10th Doctor and his attitude to give the villians one chance (but no second chances, he’s that sort of a man). For example, giving the Krillitane a single warning, similar with the Sontarans, the Sycorax and the Vashta Nerada. Eventually I would argue that the Tenth Doctor is the one to sow the seeds of saving people (for example in Fires of Pompeii, offering to save Davros in Journey’s End and killing himself to save Wilfred).
Finally, the 11th and 12th Doctors tend to have slowly shifted towards trying to help people and ‘be a doctor’. For example, the 11th Doctor trying to save Gallifrey rather than destroy it and the 12th Doctor trying to convince Rusty to become a good Dalek.
Of course, I am drawing very wide connections here and I have picked examples to fit the general idea. In reality, many episodes will have a general rule, but may break that rule to fit a particular narrative.
I haven’t even mentioned the behaviour of classic doctors (partly because I don’t feel I know enough to comment) and the 13th Doctor’s character has been a little muddled, so have also left her out.
At times, the Doctor's stance on weapons, fighting and killing can seem inconsistent. They speak out about non-violence on some occasions and then seem to kill the baddies at other times.
The Doctor who made the clearest explanation of his policy was the Tenth, who said:
"No second chances. I'm that sort of a man." - The Christmas Invasion
This concept of giving someone a chance to do the right thing before they become a victim to the consequences of their own actions was expanded on in The Runaway Bride:
DOCTOR: Empress of the Racnoss, I give you one last chance. I can find you a planet. I can find you and your children a place in the universe to co-exist. Take that offer and end this now.
EMPRESS: These men are so funny.
DOCTOR: What's your answer?
EMPRESS: Oh I'm afraid I have to decline.
DOCTOR: What happens next is your own doing.
This principle of giving his foes a chance to run has been repeated many times since - for example, Eleven gave a similar ultimatum to the Atraxi, as did Twelve when speaking to the Testimony. Both Ten and Twelve attempted to 'save' The Master in the hope they would redeem themselves.
During the Steven Moffatt era there was a lot said about the Doctor's choice of his own name, and what it means. By calling themselves 'The Doctor' they make a statement about what they stand for. A real-life doctor is committed to the preservation of life and to "do no harm". However, to save a human life a doctor may have to make a choice to end the life of a parasite, or even to make a choice between two lives of equal value. This seems to fit with The Doctor's stance. They would not do harm to anyone unless by doing so they were saving more, innocent lives.
The darkest thing the Doctor has ever done (in my opinion) was their punishment of the 'Family of Blood'. He didn't end their lives but did trap them in various eternal states of punishment. But doing so, he kept them from harming anyone again.
The 4th Doctor had the opportunity to destroy the entire race of Daleks but chose not to because he didn't feel he had the right. In the most recently aired episode Revolution of the Daleks the Doctor trapped the Daleks in a TARDIS programmed to collapse in on itself and travel to the far-reaches of the vortex - this sounds more like they were trapped in a quantum state than 'dead', rather like what happened to the Family of Blood.
To sum up - the Doctor seems driven to preserve life and doesn't believe they have the right to take it, even from seemingly evil beings like the Daleks and The Master. However, they will make the choice to save innocent people at the cost of the perpetrator's lives.
I think it mostly depends on who or what the species is. For example, he always tries to save and protect humans no matter what. When they die, it seems exceptional, or they sacrificed themselves.
The Doctor also tends to protect whatever species' really need him, like in Season 8 Episode 2, where he decided to help the Dalek, since it seemed to be good. He also wanted the Dalek to be better than the Doctor, since he didn't want the Dalek to destroy its species with hatred.
The Doctor basically helps all those who truly need him, and doesn't really kill unless it is a threat.
