I'm not clear on your question. You mention cutting the seatpost, but mention the top of the seat tube under the collar is cracked. Which part is damaged, the seatpost or the actual seat tube on the frame?
If the seatpost is cracked, don't cut it. Just replace it. A safer fix.
If the seat tube on the frame is cracked under the collar, still don't cut it! You're making a permanent solution to a temporary problem. There are a few different ways to handle the issue. The proper way would be to have it repaired.
Alternatively, although I don't necessarily recommend it, because this isn't a structurally critical area, a cheaper solution is to find the terminus of the crack and drill a tiny hole to prevent further cracking. If your seatpost holds and the crack does not propagate any further, then you're good to go. Otherwise, we can help if you need to have it repaired.