Basic principle of soldering. Water contaminates (for the purpose of adding solder) the poor joint. You can not just reheat and gob more solder on. Sure, the glob may stop the leak temporarily, but it will not last. The only way to fix the joint is to disassemble it completely and start from square one. Cutting pipe is far easier with a tubing cutter, and better than sawing, but sometimes you gotta do what you gotta do. I've used a fine metal cutting blade in my jig saw. Sure it leave a nasty burr even with the fine blade, but it can be done so the cut is reasonably square. The burr has to be removed which will take some time and effort.