stripped screw

Hi, I’ve got a joist which has taken too many screw holes now. Whats the best way to fill them without taking the board off? Or is it a case of replace the part of the joist?

Title says it all, I've got a damaged/stripped screw head in my kitchen sink tap....bad times. See photo attached. I've tried different screwdrivers with a bit of force but that thing isn't coming out and I don't want to make it worse. How would you approach this horrible task. I've...