[RICK LAKE]

ratsnst1 Any change of getting a first name? Calling you RAT just doesn't work for me.
Any way Here's what is happening. You are running along at part throttle. slam on the brakes and clutch pedal at the same time.
You have cut off the air to the motor. The fuel is still begin suck in a little longer. Too much fuel, not enough air, no fire in the hole. In the old days, carb had idle kickers. They worked off vacuum or electric to stop the idle from going below an adjusted rpm when the throttle is closed. They where also used for loads on the motor like AC compressors. In the old days when that thing kicks in the idle goes up 200 rpms because of 20 hp is being used to power this.
Fuel level in the carb, it should be in the middle of the sight glass. If it's a carb with front and rear bowls the problem is the high "G" stop is pulling the fuel away from the jets on the primary side. This causes fuel starvation and kills the motor. There is no 100% fix for this. 1/4 mile racing we had this problem alot with Holley carbs. We raised the float levels as high as we could and rubber tubed the vents to stop gas from going into the motor and washing out the cylinders. It's not pretty but works.
Clutch air gap when engagement of pedal You need a .035-.050" of air gap between disc and pressure plate. Have to remember that when the clutch gets hot, some disc get grippier and will drag down the motor under stop you are doing. You didn't say what kind of control you have for the thrown out bearing and type but the engagement doesn't happen as fast as the brakes locking up. This will also kill the motor. Rearend locks up the tires driveshaft stops spinning clutch is draggiong to release, motor dies.
Any combo of these things above will cause your problem. If this happens offen, make a bracket for an idle soleniod valve that works off vaccuum. This will control the idle under hard braking.
This is one of the reason I went to FI system, computor is alot faster that you or me and controls the motor under high "G" issues without any problems Good luck Making a bracket is not hard, use the 2 front bolts of the carb for a mounting spot. The rest will be adjustments. It's not hard, will take a little time. IMO I would leave the carb alone if the motor is running good and this is the only problem you are having. Rick L.