This sounds totally gross, but I had a number of small ones under my armpits. I just pulled them out. Didn't hurt and didn't bleed at all. I just grabbed them, and gave them a really really big yank. The way skin tags form is kind of like a lump hanging out of your skin by a stalk. If you pull really FAST and really HARD (like you are waxing your legs, for example), you'll pull it out by the stalk. I get them when they are small. If you CUT them off, you aren't getting the "root" and they will bleed like nobody's business.
I KNOW, EEEEEWWWWW!!!
But, it worked for me. They haven't recurred, and didn't bleed at all when I did it.
My SIL thinks I'm NUTS, but hey, she has them and I don't!
If this doesn't appeal at all to you, seriously try the old-fashioned way. Tie a thread (can be clear) really tightly around the base of it. You won't get gangrene or infected or anything. All this does is restrict the blood supply to the tag. It will wither away as a result and fall off. Seriously.