Yes, you can call the Get Message List API to read all messages (set messageType=VoiceMail if you only want to read voicemail messages) of an extension. Then grab all the message ids and call the Delete Message API to delete them. The delete message takes an array of message ids so you can delete them all in 1 API call. Remember to set the purge=true to delete all attachments associated with those messages. Here is an example in Node JS to delete a single message and its associated attachments:

async function deleteMessage(id){

  await platform.delete(`/restapi/v1.0/account/~/extension/~/message-store/${id}?purge=true`)

}