120 volt outlet not functioning properly
You mentionned the voltage being 120v. I assume this is when there is no load on the circuit.

Most likely, when you draw higher amperage, the voltage drops in a bad connection. This could be:


a bad backstab connection
a loose wire nut somewhere along the path from panel to outlet
a damaged wire somewhere in the path
way too long wiring (unlikely)


Since you're able to use a voltmeter to measure the 120v, you can also measure it while there's a load. (use something safer than a saw, if you're going to look at the voltmeter at the same time, say a toaster :-) ) 

Once you confirm the voltage drops, just walk back along the path, and figure out where the drop occurs. Either at the outlet backstab or at a loose nut would be my guess. 

Fix it by redoing the nut correctly or not using the backstab.

Personnaly, if I'd trace it back all the way to the first connection after the panel, I'd call the electrician.