I don't remember the name of it, but this reminds me of an arcade game I played once, where your walking through the streets fighting all the thugs that try to stop you. If your character ran out of health then the continue screen is them waking up tied to a bomb and the fuse got closer the longer it took you to put in another coin. If you do continue a knife falls from the top of the screen and cuts the fuse, but if time ran out then everything loses its color and you hear an explosion.

I think that was Final Fight.