Yes, Home Depot will rip sheets of plywood or MDF for you. They do an OK job, but sometimes it has to be cleaned up at home.
You might want to look in the phone book to see if there is a lumber store or a woodworking store nearby. You can buy wood, MDF, etc. there and most have a workshop. One around here charges $2 a cut, another charges $60 per hour. It is reasonable, though, since they use expensive pro equipment and if they make a mistake, they fix it for free. If you put together a "mill bill" of the cuts you want, you can drop it off there and they'll cut it exactly how you want.
This is a great way to go with DIY speakers, too. Also, if you ever find plans for furniture you like, you can have them cut all the pieces for you. Assembly and finish take labor, but not much skill. You'll save a ton of money over buying at a furniture store.