I don't know about your phone, but my HTC has an option to block callers built into the phonebook. I don't know whether this also prevents voicemail, but I've never received one from a blocked caller.
If that doesn't work, there are call blocker apps in the Play Store which also include options to reject or forward calls. So if "reject" sends them to voicemail, forward to a non-existent number instead and that should just give them a "dead line" tone if they call you.
Of course that won't stop them leaving a voicemail if they call when you are out of cover or switched off. That is would be something that would have to be done by the network rather than your phone, so you'd have to speak to your provider to see whether that is possible.