How to Delete Voicemails from VVM App Using Tasker
Deleting info on the Visual Voice Mail app itself was as simple as deleting the db file. This was located just above the folder containing the voice mails. It was in the format: xxx-xxx-xxxx@tmobile.db.

I used Tasker to delete that file, and then went back into the app. No more voicemail showing. 

It's probably best practice to delete the cache files as well. 

Haven't had any problems receiving new voicemail. Therefore, there's no reason to try and use an intent to do the same thing. Without the database file, the app can't find any info on deleted voice mail messages, so it thinks they don't exist.