If you tie off the blood supply to the skin tag before cutting the skin tag off then you shouldn't have any bleeding.
After you cut the skin tag off you should leave the string you used to tie off the blood supply on the skin and keep it tied off to let it heal and prevent bleeding.
They do make an easier and less risky way of removing skin tags. There's a tool for removing skin tags much easier than cutting it off.
It's called the Tagband skin tag removal tool.
The Tagband Skin Tag removal tool removes skin tags with ease at home and only costs around $20.00