Not in the simpsons game no. It's a pain but you can only save it after each level. You can go back to the house half way through a mission (press start or select) and it save it but when you go back to the mission you have to start at the beginning again
If you don't plan on using your psp between playing times you can put it to sleep and it will pause the game where you left it. Just flick the power switch up quickly and it will turn off, then when you turn it back on it will be in the same place.
If you want to use the psp to do something else then this doesn't work.