You can spend some of the unspent outputs or you can spend all of them.  Regardless, once you import the private key into a wallet on a computer you should dispose of the "paper wallet".  If there are any funds left in the wallet on the computer when you are done with your transactions, and if you want to return those funds to a "paper wallet", you can create a new "paper wallet" and create a transaction to assign the remaining unspent outputs controlled by that imported private key to the new paper wallet.