No, a mediator cannot have the support stopped. You have an order for support. The only way for that order to be modified is by another court order. Until your daughter reaches the age of 18, both parents are financially responsible for her. Dad cannot get out of paying support and certainly cannot get out of it simply by requesting that during a mediation. It's good that you have a wage assignment order. Stay on top of it. Make sure that first payment comes and continues. If Dad changes jobs, you'll need to request a new wage assignment order.
I personally have never seen a child support matter go to mediation because the state uses guidelines that are pretty hard to deviate from. he may try to file a motion to set aside default but if assuming the judgement was correct to begin with ( using his correct income) it wont lead him anywhere. Mediation is usually ordered when parties are in court for custody and visitation. The courts want the parents to work out a parenting plan on their own if possible. If the Department of Child Support services is involved, they will take care of collecting the support money from his paycheck otherwise you have to obtain an order to garnish his wages and serve his employer. Hope this helps. Feel free to email me at email@example.com for more info.
The advise given herein is for informational purposes only and should not be relied upon as legal advise without further interview with the lawyer on the details of your case. No attorney client privilege or relationship is created by virtue of this forum and my response to your inquiry. Please email firstname.lastname@example.org for more information or assistance.