Is there a way to kill something without putting it in the kill ring? It's probably my biggest pet peeve about emacs that there's no way to kill text without emacs assuming that you want it somewhere else.
M-x delete-region by default (although you can bind it to anything).
I use emacs every day, and don't think I've ever used it though. Just put the stuff you want to delete in the kill ring.
Why don't you want stuff in the kill ring? It takes some getting used to, but I've found it's generally a good thing. You can always yank back previous items in the ring with M-y too, so it isn't like your OS clipboard where 'cutting' something else means you lose access to the previous item on the clipboard.