You will need to use solo-mining with spreadcoin daemon. To get your mined coins you will need then either download wallet.dat or send coins to your wallet using command-line. Currently there is no way to mine running network node on one computer and miner on the other.

Here are instructions how to run solo-miner in case you don't know.

Set user and password in ~/.spreadcoin/spreadcoin.conf

Launch spreadcoind daemon.

Then you can start mining using the following command:
and stop using:

If your wallet is password protected you will need to unlock it using walletpassphrase command.