Use styptic powder or even flour to stop the bleeding.
Did this happen while you were cutting the nail? If so, then the trimming was too close to the quick (blood vessel inside the nail). When cutting, make sure you look at the nail and find where the pink area is. If you see pink inside the nail, that is the quick - Don't cut too close, especially if your rabbit is not used to getting its nails trimmed. If your rabbit has dark nails like mine, then you will need to use a small light to look through the nail to find the quick. I personally use a small pen with the light at the end of it.
One of our disabled girls quickly jerked her leg back while we were trimming her nails (snuggled in a towel). Her nail came out at the base! We used pressure to stop the bleeding. I can't recall if we also applied styptic powder or flour ? Her removed nail area was monitored for infection as time went on. We got thru A-OK. 'Tis a scare, for sure!
This has happened to Theo before, and it was not while clipping his nails. I applied pressure and flour and it worked great. He didn't lose the nail, it just started bleeding while he was running around. I still don't know why it happened, but it healed up perfectly.
Thank you I googled it real quick and put flower! She’s doing better. My phone light blinds me when I clip her nails. I can’t see I only see spots so then I clipped the nail to close she I didn’t rip it.