I attempted to solder an outdoor spigot to the water supply line. All looked good until I tested the water flow. There is a small spot I missed. Water spurted out. Can I re-solder the pipe without have to take the whole thing apart and start all over?

Yes, and flux to the pipe and go again, open the spigot iit get the water out. The only way you might have a problem is if the wart is trapped in a low point and you can not get it out before soldering.

Put heat to the faulty connection and boil the water out of the pipe. When steam stops try pulling the joint apart. Wipe off the excess solder with a dry cloth and shine the pipe with a piece of sand cloth,
Flux the pipe and try again. Good luck, Tom