Last Tues, June 16th, I signed a lease for a 1 bedroom 1 bathroom apartment that would be available to move in on Thurs June 25th. The apartment office called me today to tell me that the apartment that I signed the lease for would not be available because the current tenant is no longer moving. They offered me another 1 bedroom 1 bathroom apartment that won't be available to move in until July 2nd for the same price as the one I signed the lease for or I could upgrade to a 2 bedroom 2 bathroom apartment and move in on my scheduled move in date of June 25th but its going to cost me $50 more in move in costs and $60 more a month for rent. Also they have a 60 day move out policy where you have to give them 60 days notice that you are leaving and the current tenant gave them that notice and then told them the week she was suppose to move out that she is not leaving. They told us by law they can't force her to move. Is what they are doing legal?

No, you can not force them to move.
** in theory perhaps the apartment complex could, but that is another issue.

You have the choice, they have broken the lease with you, you can ask for them to return all of your money.

I personally would ask them for a upgrake free, since they are breaking the lease

In my apartment lease contract there is a clause stating that they are not responsible for the delay of occupancy due to construction, repairs, cleaning or previous residents holding over. Now I am being told that the apartment that I signed a lease for will not be available at all because the current tenant is not moving anymore... Does this clause apply since I will not be able to move into that apartment at all?

Please don't start a new thread. I've combined both of your threads so that all of the information will stay together.

Carefully re-read that clause. In fact, it will be helpful if you give us the specific language. Because what you've said is that they are not responsible for "delay". It doesn't say "non-delivery". In your case they are not delayed. They can't deliver at all. If the clause says nothing more than that, then it doesn't apply to your situation and they are breaching the lease.

If you want to stick with a 1 bedroom, tell them you'll take the other 1 bedroom but you want 1 month free. If you want to try for the upgrade, tell them you'll take the 2 bedroom but at the same rent and move-in cost as the 1 bedroom.