No. Your Ex’s right to visitation or access to the child you have together will generally be based on a Court Order – as will his or her obligation to pay child support. But unlike a regular contract, where a failure by one party to stick to the terms can mean the contract is breached and “all bets are off”, a breach of a Court Order is addressed by specific judicially-imposed remedies.
So if your Ex chooses not to follow the terms of the Court Order that governs his or her child support obligations (or any other term) then you are not allowed to simply take matters into your own hands by cutting off his or her visitation rights, or imposing other consequences. You remain bound by the Order even if your Ex has breached it. Your recourse is to apply to the court for enforcement of the strict terms and obligations under the Order.