Let me preface this by saying that I do tech work on amps.
What you are describing sounds like severe crossover distortion. This is caused when either 1) your power tubes are severely mis-matched; I've seen brand new supposedly "mached" Mesa tubes that were at extreme oposite ends of the scale; or 2) One tube is just not working at all. The most common cause of this is a bad screen grid resistor, I've seen it happen quite a few times.
A two or more tube amp can work and actually almost sound ok with 1 tube not functioning (but in the circuit), except you'll get a bad distortion/hum that fades in as the note decays. The broken screen grid prevents the tube from flowing current. It will still light up, have plate voltage, etc, but not flow signal.
If you have an extra set of power tubes, you can put them in and see if the problem goes away. If it doesn't, its probably a bad screen grid resistor. I do not recommend Mesa tubes by the way; the quality is generally pretty bad. If you want tubes to work in your non-adjustable bias Mesa, just make sure your specify "medium bias range" matched tubes when you order from Tube Depot, Tubes and More, whoever; or get a Groove Tube that falls in the 4-6 range. I recommend JJs since they are a very robust tube that will put up with a lot of abuse. That would be a Groove Tube with the "S" designation; ie. GT EL-84 S.
If all that is greek to you, and since its under warranty, call Mesa and find out how to get it to an authorized repair center, and give them the information above.