I’m writing a script that requires an actor to punch and crack a mirror that would leave his hand bloody… but… how can I go about shooting that without actually damaging the actors hand? I don’t exactly have a huge budget here, so the cheapest possible way would be best. 
Being able to actually see the hand connect rather than a sort of cutaway would be preferred.
I spoke with the partner Slip (who’s been in props for a long time) - we would guess that you’re looking for a film prop, judging from the description?
The toughest part is going to be avoiding damage to the actor’s hand - even with breakaway glass or a Plexi mirror, there still is the possibility of injury.
The partner’s recommendation is using a Plexi mirror that is cut and repieced. He said that if it is well pieced, the seams are difficult to see. If you have to see the mirror first, perhaps a cutaway shot there - use a real mirror to establish its presence, then replace it right before the punch?
As for the blood, given that the blood would look most natural on the knuckles, perhaps a blood sponge in the other hand - the actor punches, grabs his hand (thus bloodying it), and then presents it for view? Or, alternately, the actor has a blood pack, breaks it, and lets the hand hang (so there’s lots of blood dripping down).
A resource where they discuss these things all the time (albeit usually for stage) is “Society of Properties Artisan Managers” (AKA SPAM). They have a listserv that has these sorts of questions flying back and forth.
His final recommendation is write it, and let the props and FX guys figure out how to do it
Yeah, you don’t wanna to it “Apocalypse Now” style. Martin Sheen actually punched a real mirror and really cut his hand and really bled all over everything. They kept the cameras rolling through the whole thing.
Maybe you could also use a prosthetic hand or skin tone thick glove for the actual swing shot.
You could build a Plexi Mirror that is broken from behind. If you sandwich a pane of glass between a mylar and plexiglass, you can use a levered weight to crack the glass. I’m sure there are plans for such mirrors out there, but my google-fu doesn’t seem up to snuff today.
Anyhow - You have a mirror that is broken from behind by a stagehand (make sure there is plexi on both sides for safety’s sake.). With proper staging you can make sure the actor never even touches the mirror as the cue for it to break is called.
Apply blood to knuckles as needed.
Freudian_Slip’s post makes me wonder if you’re filming or doing this on stage.
I’m going to be filming this… all the suggestions are great. Doing the Martin Sheen (actually punching a real mirror) is tricky business. He was getting paid a lot of coin though. I’d punch a real mirror for his paycheck. Hell, I just might punch a mirror because I’m NOT getting paid that much. 
It wasn’t scripted. He was extremely drunk and just drunkenly punched it. He let Coppola keep all of the footage afterwards - the naked dancing / moaning / crying / punching - all unscripted drunkenness.
I’d use a mylar balloon.