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.
In this scenario where funds are left over from a transaction, is the recommendation to transfer those funds to a new paper wallet to avoid storing the funds online?
If that is what you desire to do.
Which is why I said:
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.