First of all, unless the doctor is providing the procedure as a gift then the transaction is a contract. Every transaction where valuable consideration is provided by 2 or more parties is a contract: buying chewing gum from the supermarket, lessons from a tennis coach or advice from a lawyer - all of these are contracts as is every medical procedure a doctor performs for which they get paid.
In my experience GPs do not generally use written contracts; surgeons almost always do.
The general common law position is that the parties to a contract can agree to anything they want provided it is not illegal.
Signing the contract will almost certainly reduce the doctor's liability but only down to what the law in your jurisdiction permits.
It is a fair bet that there is a whole body of law in whatever jurisdiction you are in that limits the amount of liability that a service provider like a doctor can avoid under a contract - if those limits are respected in a contract then they will be binding on the parties; if they are not then the entire contract may be invalid, or, if it is a well drafted contract, the invalidity will be limited to the unlawful terms.
You basically have 3 choices:
- Sign the contract and accept the doctor's terms
- Negotiate different terms acceptable to both of you
- Find another doctor
Starting from a common law basis, a doctor is under no legal obligation to perform a procedure. That said, there are many jurisdictions that do impose such an obligation to render emergency aid, however, most of these are drafted such that the person compelled to perform the service is indemnified except in cases of gross or criminal negligence. Such laws are referred to as "Good Samaritan" acts.