In case you missed the implications of the R rating or the fact that this film is about one of the most famous serial killers in all of comics history, Joker is a fairly bloody movie.
It's disturbing and perverse, but it doesn't wade into Tarantino-like exploitation waters, mercifully, and unlike the comic book movies that kill cannon fodder for effect, every death in it matters to the narrative. They range in type though and it's worth going through them all to explore what they mean and which ones left the biggest marks...
OBVIOUSLY, SPOILERS WILL FOLLOW FOR JOKER.
7. The Innocent Clown
We don't ever get to learn his name, but the clown protestor killed on the Gotham train when Arthur escapes from Detectives Garrity and Burke (wonderfully cast, but woefully underused) is the real trigger moment for Gotham burning. It's also an important moment in Arthur's transformation.
Up until that point, Arthur felt kinship with the clowns without feeling a part of their movement - as he says, he "believes in nothing" - but seeing the clowns effectively protect him (at least that would be his take) reinforces the final change in his character. It's that moment that turns him into Gotham's clown prince.
The death itself would be the central tragedy in another movie - an exhibit of police brutality - but it's almost throw-away here. He struggles with Burke as he pulls his gun and ends up shot and killed. A harsh end, but an important moment.