The problem with Spock being officially considered the second mutineer in Starfleet is that every time that Commodore Mendez wanted to say "Arrest Spock for mutiny!" the Talosians, if they wished to, could make those around him think that Mendez said something different or didn't say anything at all.
In "This Side of Paradise" the crew fall under the influence of the Omicron Ceti spores and desert the Enteprise:
KIRK: Get back to your stations. Get back to your stations.
CREWMAN: I'm sorry, sir. We're all transporting down to join the colony.
KIRK: I said get back to your station.
CREWMAN: No, sir.
KIRK: This is mutiny, mister.
CREWMAN: Yes, sir. It is.
KIRK: All right, you mutinous, disloyal, computerised, half-breed, we'll see about you deserting my ship.
But if there were any legal actions the verdict would have been not guilty by reason of temporary insanity caused by the spores.
In the third season of TOS "The Tholian Web" was the 65th episode produce and was aired on 15 November 1968 and started on stardate 5693.2, and "Whom Gods destroy" was the 72nd episode produced and was aired on 3 January 1969 and started on stardate 5718.3. Thus "The Tholian Web" seems to be earlier than "Whom Gods Destroy" in production order, airdate order, and stardate order.
In "The Tholian Web", on the bridge of the Defiant it looks like the crew all killed each other.
(The crew are dead. One man is in the act of strangling another.)
CHEKOV: Has there ever been a mutiny on a starship before?
SPOCK: Absolutely no record of such an occurrence, Ensign.
MCCOY: Jim. The Captain's neck is broken.
If there was a mutiny on the Defiant it was because the crew were driven insane by the effects of the interphase. Thus the verdict would be not guilty of mutiny because of insanity caused by the spatial condiditons.
"Space Seed" was the 25th TOS episode produced, aired on 16 February 1967, and had an opening stardate of 3141.9. "This side of Paradise" was the 26th TOS episode produced, aired on 2 March 1967, and had an opening stardate of 3417.3. Thus "Space Seed" would have been before "This Side of Paradise" in all three of the usual episode orders, production order, airdate order, and stardate order.
Why does this matter? Because Chekov became a member of the bridge crew and was seen in many episodes, starting with the second season, but was never seen during the first season. In Star Trek II: The Wrath of Khan Khan and Chekov recognized each other, even though Chekov was never seen in "Space Seed". The simplest explanation is that Chekov was part of the crew during part of the first season, and Chekov and Khan met off screen during "Space Seed".
And so Chekov would probably have been aboard during "This Side of Paradise" and thus would have jumped ship while controlled by the spores.
So in "The Tholian Web" Spock could have answered Checkov asking "Has there ever been a mutiny on a starship before?" by saying "Yes, on the Enterprise at Omicron Ceti right before you came aboard.", or "Yes, and you were a part of it.", or "Yes, even though you do not consider your behavior at Omicron Ceti to have been part of a mutiny merely because it wasn't violent.".
But Spock didn't say any of those things. Thus like Chekov, Spock didn't believe that a nonviolent mass desertion by a starship crew constituted a mutiny. Spock obviously believed that a violent attempt by crew members to illegally and forcibly seize control of a starship was necessary to be a mutiny.
In "Whom Gods Destroy" the insane Captain Garth has taken over the asylum on Elba II.
GARTH: My crew mutinied. The first use I will make of the Enterprise is to hunt them down and punish them for that.
KIRK: The crew of the Enterprise will also mutiny.
This is later explained:
KIRK: And tried to destroy Antos Four.
GARTH: Well, I could say because they were actively hostile to the Federation.
KIRK: Yes, you could say, but that would be untrue.
GARTH: Agreed. Actually they were quite harmless, and they made me whole when I was maimed and dying. And in my gratitude, I offered them the galaxy. They rejected me, and I condemned them to death.
SPOCK: How could you, a Starship fleet Captain, believe that a Federation crew would blindly obey your order to destroy the entire Antos race, a people famous for their benevolence and peaceful pursuits?
Clearly the insane Captain Garth ordered his crew to commit genocide, an illegal order, and they refused that illegal order and restrained him. So there was actually no mutiny involved.
So according to the available evidence, there has been no mutiny on a starship up to the third season of TOS. Since Spock said it, it must be true.
But on the other hand Michael Burnham was apparently convicted of mutiny in Discovery and Spock's actions in "The Menagerie" were called mutiny by various persons.
SPOCK: Captain Pike, may I remain for a moment? (flash, the others leave) You know why I've come, Captain. It's only six days away at maximum warp and I have it well-planned. (flash, flash) I have never disobeyed your orders before, Captain, but this time I must. (flash, flash) I know. I know it is treachery and it's mutiny. but I must do this. (flash, flash) I have no choice. (flash, flash)
SPOCK: The charge is mutiny, Doctor. I never received orders to take command.
KIRK: A mutiny requires a trial board of no less than three command officers. Since there are only two of that rank available
Captain's log supplemental. Mister Spock, on trial for mutiny, has forced the court to accept unusual evidence. On our monitor screen, the voyage of Captain Pike and the Enterprise to the one forbidden world in all the galaxy.
But in the end the charges were dropped.
UHURA [OC]: Message from Starbase Eleven, sir. Received images from Talos Four. In view of historic importance of Captain Pike in space exploration, General Order Seven prohibiting contact Talos Four is suspended this occasion. No action contemplated against Spock. Proceed as you think best. Signed, Mendez, J.I., Commodore, Starbase Eleven.
So either Commodore Mendez decided to drop all charges against Spock, or else Mendez still wanted to try Spock for mutiny but the Talosians prevented everyone from hearing or seeing his orders to do so.
But Spock would know what he did, just as he would believe that his stepsister Michael Burnham had committed mutiny. So why did Spock say there was no record of a mutiny on a starship?
In my opinion, Spock believed there was a difference between "an act of mutiny" and "a mutiny". "An act of mutiny" could be committed by one single person, while "a mutiny" required two or more crew members conspiring to seize control of the ship illegally.
Thus Spock could believe that individual starfleet officers had committed "acts of mutiny", but that there had never been "a mutiny" on a starship. And that may seem a very technical and nit picking distinction, but in many trials the life or death of the accused has depended on such technicalities.