Tanto quanto me lembro, não .
A única morte que acontece no desenho animado está no episódio Blue Cat Blues , onde está implícito que ambos eles cometem suicídio no final do episódio (na verdade não é mostrado).
De Mortes controversas dos desenhos animados:
This is not the typical episode about Tom & Jerry. Tom falls madly in love with another cat and showers his sweetie with all sorts of gifts including jewelry and even a car -- but she doesn't seem to be impressed with his meagre fortune. He even signs away his arm and a leg for her, but alas, to no avail. When things go awry, he later becomes an alcoholic. Why? Mr. Butch (Tom's rival) stole his love away from him.
The heartbroken Tom winds up in the gutter and sadly, Mr. Butch ends up marrying Tom's only true love. Of course, all of this is narrated by a 1950's deadpan voice, which adds to the eerie feeling of the short clip.
The episode ends off with Tom on the train tracks with a train approaching... This is definitely not a pick-me-upper.