What it means
Ham-fisted means clumsy, rough, and short on finesse. You throw it at someone who handles delicate stuff with brute force and a weird confidence, whether they're wrapping a present, fixing something fiddly, writing an apology, or trying to calm a situation down and somehow stomping it flatter. It's usually mocking and paints them as all shove, no touch.
Usage examples
"She made a ham-fisted job of wrapping the gift, paper and tape everywhere."
"His ham-fisted attempt at an apology only made the whole thing worse."
"His ham-fisted attempt to wrap the present looked like the paper had lost a fight with the scissors."
"Don't let Dave near the cake icing, he's too ham-fisted and it'll end up looking like plaster."
"Her ham-fisted text trying to calm things down just poured petrol on the whole mess."
Where it comes from
Recorded in English from the 1920s, ham-fisted grew out of the comic image of someone having hands like hams, thick, heavy, and hopeless at fine work. It caught on as a lively put-down for people who blunder through careful jobs with force instead of finesse.