Is there a tension screw on the pedal?
It's an allen key headed screw normally - if yes slacken the tension right off and then get some Mole Grips on the cleat and try to twist it out using the same motion you would use if it was still attched to your shoe.

Training fail this week was a puncture on the way home going at speed trying to race the fading daylight to home. 30mph downhill with no air in the tyre was a little too exciting....
Managed to replace the inner tube but hands got filthy and frozen, realised just in time I was just about to freeze my fingers to the CO2 cannister.
A few miles further on felt the familiar bump/thump of another puncture. Poor light and no feeling in my hands meant I hadn't spotted a tiny but sharp flint still poking through the tyre just enough to puncture my brand new spare tube.
Adding that mistake to getting rained on three times when the forecast was "10% chance of rain" meant I wasn't a happy chappy.