How do I completely mute the sound in phone calls?

I don't mean I want to mute the ringtone, and I don't mean I want to mute my own microphone. I want to mute the sound of the *other person on the call*. When I use the volume control during a call, I can put the slider all the way down to zero but the call is still audible - either the slider only acts on the ringtone, or the slider is capped at a minimum (non-zero) volume level. How do I make the call completely silent? (For context: I make calls using a relay service, where I type, and a remote assistant speaks and types the response back to me. This service involves making the call on my phone, so I still get the sound of the people talking - I want to silence this.)