Mildly. Trainer Betty Schumacher would sometimes lose her patience with Tonto and flick at his nose, sometimes inadvertently hitting him, which both Art Carney and director Paul Mazursky said they would not tolerate. For the scene at the end when Tonto dies, the cat was given a sedative.
It's unclear if Tonto shown at the end is dead or is just sleeping, but he's motionless, and then Harry mentions in a letter that he passed away. In reality, the cat was just sedated.
Harry is mugged near the beginning. He isn't beaten up, but the younger man takes advantage of him and throws down his groceries when he won't give him money.
Harry is forced out of his apartment by the city so the building can be demolished. He briefly lives with his son's family before setting off on his own. He spends most of the movie hitchhiking across the country.
Tonto dies at the end, likely of old age. Harry last sees him in a cage, presumably at a vet clinic. He sings him a song and they show Tonto motionless.