Is there any way to have wage garnisments stopped after it has been started?

You could ask the garnisher to release the garnishment if you have made arrangements to pay to their satisfaction; it isn't a dismissal and it can be started again quickly. Or you could settle and pay off the debt. Or you can file bankruptcy.

You can pay them in full what you owe them, you can challenge the judgement on some legal grounds and get the case dismissed, but once it starts, assuming the you really owe it, and that the legal action was done correctly, you can file bankruptcy or get some other legal stay to stop it.