Saying for using an overly powerful tool to fix a minor problem
I found "A sledgehammer to crack a nut" as one example. What are some others?
Consider,
a [sledge]hammer/cannon/shotgun to kill a fly
Ngram
a nuke to kill a fly
Mathematics StackExchange
a [cruise/nuclear/heat-seeking] missile to kill (or zap) a fly
Google Books
Consider "to break a butterfly on a wheel":
Who breaks a butterfly upon a wheel?
A rhetorical question referring to an excessive amount of force that has been applied to achieve something minor, unimportant, or insignificant.
To "break upon a wheel" refers to a mode of torture, in which a victim has his or her bones broken while strapped to a large wheel.
(The Free Dictionary)
If a single word is OK, try overkill:
An excess of what is necessary or appropriate for a particular end
(AHD)
Also, you can use a sledgehammer to swat a fly, too.