Now the microwave is now in a new location so we have to extend the circuit. The microwave only requires 15A's. Can I splice 14/2 to 12/2?
Many don't seem to agree with my input but here it goes, First of all stick with the same wire size because its fool proof and will keep you out of trouble.
technically the #14 rating is roughly 1850w, if never exceeded it would be safe, until someone decides to continue out of that box with additional loads which can happen, they'd now have a 2400w rated breaker allowing for an 1850w rated conductor to provide more service.
Not mentioned but as, if not more of a concern, the extended splice still needs to be accessible, don't be like the jack of all trade master of none handyman and bury the splice in the wall or behind a new cabinet.
The wiring will only utilize what the load requires.