Your use of the [Services (that) we provide] constitutes the subject-matter of the contract.
No, you should not separate "we provide" by commas, because it is a restrictive relative clause. It is too tightly bound with the word "services".
You can separate by commas a non-restrictive relative clause - a clause that provides additional information:
Your use of the Services, which we provide to anyone who needs them, constitutes the subject matter of the contract.
In this example, it is implied that the reader knowns what the services are and therefore the part between the commas could be omitted: it is merely a "comment".
Moreover, in English only a restrictive relative clause (that uses no commas) can have its relative pronoun ("that we provide") omitted:
Your use of the Services, we provide to anyone who needs them, constitutes the subject matter of the contract. (WRONG: you need to use the relative pronoun which, because the relative clause is non-restrictive)
You can theoretically add the relative pronoun which to your clause and make it non-restrictive, but it will look strange in this role, especially in a legal text:
Your use of the Services, which we provide, constitutes the subject-matter of the contract. ("Oh, and by the way, it's we who provide these services")