There is not a format option per say on the ps2 that I am aware of. What you are capable of doing is going into the system and deleting whatever you do not want to keep.
Start your ps2 up without a disc in it. You should have an option to browse. When you go into this option it will show you the memory card or memory cards. Choose the memory card that you want to delete info from. It will now give you options to delete or copy information. Delete the information. If you have files that you want to keep and you do have another memory card, you can copy them to the other card so you can keep that information. I hope that answered your question.