Depending on where you cut, the wound may bleed for a while. The last time I cut, it took quite a while for it to stop bleeding.
If the wound isn't closing on its own, it will need stitches. Use your discretion. If you feel like - if you've cut before - it is different from your other cuts that haven't needed stitches, you should probably get them!
Also, this is just an extra thing being thrown in here, but I feel like it's necessary. If a cut is deep enough that you have to wonder if it needs stitches, not only does it probably require them, but be mindful of infections. Like tetanus, depending on what you've used and how well you cleaned it - or didn't clean it - before cutting!