Is there a specific term for this?

Replacing a vulgar expletive with a substitute more suitable for mixed company or tender ears. E.G.: shucks, shoot, darn, fudge, dagnabit, etc. Euphemism seems too generic.

Bowdlerism, bowdlerization - usually in reference to doing it systematically to a work of literature, a movie, etc.

But I think just euphemism is correct too.

“Minced oath”

Isn’t the OP the exact definition of euphemism?

Bowdlerizing didn’t always or even usually provide a softer word: it cut the offensive passage of the text. Minced oath is more narrow than euphemism. It does cover the words used in the OP, though.

Edited because of being ninja’d.

I think “minced oath” is it. It’s also interesting to see minced used in another word related context along with “mincing words”.

Nevermind

A euphemism doesn’t have to substitute for a vulgar expletive, just for something that people might not be comfortable saying bluntly (e.g. “passed away” for “died”).