A loop pedal can do something like that.

I've got a line 6 JM4 and on that you can record samples and stop / start them by pressing a footswitch. You can also load in samples from an SD card. You can also connect the JM4 directly to the PA.

I'm sure a couple of the other loopers like the Boss RC3 or RC30 or the Digitech Jammans can do something like this too.