I can never get rid of the voicemail notification and I routinely hit it by accident on my lockscreen or when I pull down the notification shade. I use Google voice for my voicemail but this is my carrier voicemail giving notifications
What phone do you use? And out of curiosity, what carrier? If you're running Android, you should be able to turn off notifications for whatever app your carrier uses for voicemail. I can turn off notifications for Visual Voicemail with T-Mobile on an LG G4.
OS version, Android skin, the app, and even the carrier may all affect your ability to turn things off.