xDM

How to delete a master record of a fuzzy match entity with rest API?

You can use the Manage a load, setting the action to DELETE_DATA and setting the recordType to MASTER

Try something like this:

{
   "action":"DELETE_DATA",
   "deleteOptions":{
      "deleteType":"SOFT_DELETE",
      "recordType":"MASTER"
   },
   "deleteRecords":{
      "Customer":[
         {
            "PublisherID":"CRM",
            "SourceID":"1234"
         }
      ]
   }
}

And don't forget the Integration Guide for complete REST API details.