New bike or New tires?

How new?

If this is your first triathlon, I'd suggest just getting some slick tires for your mountain bike.

If you enjoy the experience, then look to get a used road bike for future races.

2 cents.

I agree with mrcurtain, don't bother buying anything for your first tri.  Go out, have fun, see if you like it and then decide what you want to do.  Obviously we love the sport, so we're bias, but we're aware it's not for everyone.  You might find the road biking and road running boring and go the Xterra route, then you don't need a road/TT bike

x2 if you're going out for a sprint...leave everything as is.  Knobby tires won't kill you that bad.  For an olympic, you might want to get slicks, but I say save it for beer money.

You're in college and tris can be a huge investment.  And when you're in college, you're interests are constantly changing as you try new things.  My advice would be to just have fun your first couple of races before you invest too much money and realize you rather just drink beer and chase girls...=)

Only you can answer that question based on your personal set of financial circumstances, values, and priorities.

A new set of tires is probably cheaper than a whole bike. The road bike will be faster than the MTB with slicks.

Often people find a road bike more fun to train with when riding on the road as it will be lighter, faster, and more responsive when on pavement.  That might be a consideration. Also, if you like to train with others on the road, the MTB can make it difficult.

Do you like cycling?  If you bought a road bike, would you use it?

If you are comfortable on your MTB and it works well, just get slicks. For your first few tri's, all you need is a bike, doesn't really matter which one. Just have fun and enjoy keeping in shape. Later, you can go out and get a new (or used) road bike and really start to get competitive, but in the beginning, it needs to be all about fun and a fantastic learning experience that will benefit you tremendously in the future.