Although I'm not quite an expert, here's what I'd do:
- Use pressure to stop the bleeding. Alcohol is also another option, but if it's a deep wound, it shouldn't be used.
- You do not need to cut the toe unless it's injured and really infected.
- I heard that Neosporin is also another option as long as it doesn't have any painkiller in it.
Like I said, I'm not an expert. We've had issues with blood on the toe, but it's not similar to your situation. I've only ever dealt with Bumblefoot, but never with a toe hanging off.