Yes, that does happen sometimes, especially if the cat has ever had a bad experience where a claw clipping resulted in the quick being cut into. Something like this might help:
My boy dislike having his paws touched so it's also hard for me to trim his nails. I trim his nails after he has gone to sleep for awhile and when he looks like he's in a deep sleep, that is the time I go trim his nails. I do not trim all the nails at once because as soon as I enter the room where he is sleeping, he's sort of awake but a little drowsy still and I quickly trim off as many nails I could trim. Those that are not trimmed, I leave it to another day.
This is one other way to trim your cat's nails, do it when she's asleep.
This is how you gently squeeze the paw to get the nails out and you just clip off the tip will do. Don't go too deep as you may cut the quick and cut the nerves and your cat's nails will bleed and it'll be painful for her and also it'll be harder the next time you want to trim her nails because of the painful experience. Have some cornstarch to standby just in case you cut too deep and if if do, stick the nail into the corn flour to help stop the bleeding.
Use a nail trimmer for cat..... And try feeding the cat treats while doing so. Give her treats before trimming to calm her down. Give her after trimming so that she thinks that it's a reward.