When you have a connected table you are never allowed to delete records manually or with a API. The whole point of a sync table is to be in Synch with the source table.
If your source table was a csv file, then you could load a csv with no records in it, and set the Sync to mirror the csv file exactly ands that would purge the table. That is the only way I know.
If the source was another type of cloud based source or a Quick Base table, you could adjust the filer on the Sync and set it to a way that would not allow any records in. That would also purge the table if the Sync was set to mirror the source table as opposed to add to it.