Welcome to Orchid Board Katie May
You haven't said, but I'm assuming your orchid is a Phalaenopsis. If you are not sure then posting a picture here may help us work that out for you.
If so then I don't advise cutting the existing spike to try and get it to bloom again from there. This is a method of forcing flowers, but sometimes it can weaken the plant, if the plant is not ready/strong enough to grow more at that time.
Instead I either leave the old spikes to see if they want to grow more flowers (if they turn brown and dry then they won't and I just cut them off) or I cut them off anyway right down at the bottom. If you cut them off at the bottom the plant will grow a new one when it is ready to flower again.
Anyway, that's my preference
Hope you have a great time on Orchid Board, I'm sure you will!