Been there as well. I freaked out because the blood didn't stop bleeding for over a few minutes even after applying tissue and pressure to the nail.
That day onward, I bought that styptic powder for future emergencies. I also bought the smallest nail trimmer with the safety plate. The plate doesn't do much because Scottie's nails are so small. I only trim by the slivers now, but more frequently, just in case. Scottie's a big scaredy cat! Sometimes I only do one paw a day because he's so impatient and freaked out. Other days, he's so calm he falls asleep while he's 'getting his nails done'.