Well, it depends on what timeline we are talking about.
Pogo is nothing like normal butlers in wealthy families, even though there is hardly anything normal about the Umbrella Academy. A "humanized" chimp able to talk, he was a mentor for the chaotic siblings adopted by Sir Reginald Hargreeves, clearly capable of empathy a lot more than the eccentric billionaire.
Still, Pogo had no other way but to keep Reginald's secrets, to the great discontent of some family members. Among such siblings was Viktor Hargreeves, who used the name Vanya at the time when his childhood trauma resurfaced to the extent that pushed him to go full atomic bomb mode. When Viktor discovered his immense powers, he unleashed his anger on his toxic family, and Pogo was no exception.
In the original Umbrella timeline, Pogo is indeed dead, gruesomely killed by Viktor, who threw the chimp butler on the deer horns on the wall.
But things are different in the new timeline, where the Umbrellas are substituted with the Sparrow Academy. Pogo used to be their teacher as well, but he was fired by Reginald Hargreeves after the billionaire accused him of being too protective of the Sparrows. Following his exit from the Sparrow Academy, Pogo took up… inking other people.
In an unexpected makeover, the Sparrow timeline Pogo is quite a tough guy, who ends up tattooing a sigil on Number Five's body – something that is going to be a clue for the universe reset. Killing this Pogo surely seems to be a challenging thing, but, to be fair, Viktor Hargreeves did not try to do it this time.
Now that season 3 has effectively rebooted the universe, Pogo's fate is once again unclear. It's unlikely that the Umbrellas came back to the very same timeline they originally left, so Pogo is technically a Schroedinger's chimp: he might either be dead, alive, or non-existent.
'The Umbrella Academy' season 3 is currently streaming on Netflix.