Ignore call without declining it
The best I've come up with is to hit the Volume Down button on the side of the phone during a situation like this. That causes the phone to stop ringing/vibrating, but doesn't decline the call right then and there (maybe this is what you referred to as "mute a call"?). The incoming call will last the normal amount of time before being sent over to voicemail. However, this leaves the incoming call screen active and blocking whatever you were previously looking at.