The AIM-120 is an air-to-air missile, not a MANPAD, with a 90+mile range in the latest variants. Speed is Mach 4. You are not outrunning it with a Mach 3 capable aircraft, particularly when aircraft accelerate slower. You are not going to be cruising around at very high speeds due to fuel consumption issues. So, you detect the launch, by the time you get your MiG up to Mach 2 or 3, you've been hit already.
And a MiG-31 is not going to outmaneuver anything. The AIM-120 includes a track-on-jamming mode as well, with auto-switchover to that mode if jamming is detected.