Are you using the basic non-visual voicemail or the visual voicemail?
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
Being able to remove the messages that you have on your phone is an easy process for our customers and we want to make sure you are able to complete this step. With regard to the device and removing messages please use the following link to complete this process https://www.verizonwireless.com/support/knowledge-base-208386/. JasperM_VZW