If there is no contract, can money be refunded before services are performed?

What you really mean is that there is no written contract. However, a contract does not need to be in writing to be enforceable. All a contract is, is an agreement between two or more parties to do something--for example, that party A will fix a car in exchange for party B paying an agreed-upon amount. To form a contract, all that is necessary is that there is an offer (for example, "I will fix your car for $650"), acceptance of that offer (for example, "I agree; thanks"), and an exchange of consideration, which can be things of values, promises, or both (for example, his consideration is his promise to fix your car; your consideration was half the money up front and a promise for the other half).

From what you write, all the elements of a contract exist and can be found, which means that there is an enforceable agreement between the two of you for him to fix the car in exchange for $650. That does not mean that he can't agree to let you out of the contract for  a lesser amount--such as keeping thhe $325 already paid--but it would seem that the mechanic could force you to go ahead and pay him the rest, too.