The key differences between petrol and diesel engines is the method of combustion.
Petrol ignites with sparks or with compression. Diesel doesn't ignite so well, but burns much better through compression.
Petrol engines inject the air/fuel mixture and then use spark plugs to ignite the mixture just after a piston reaches top dead centre.
Diesel engines compress air, and then add air/fuel mixture. As a result they run hotter. The compression and heat give combustion, rather than flash ignition.
The differences between the fuels are measured on the octane or cetane rating.
Fuels with a high octane have a low cetane and are easy to ignite, so work well in petrol engines.
Fuels with low octane and high cetane ignite by combustion so work well in diesel engines.
I've heard that a very small amount of petrol (0.5L in a full tank) can actually improve the efficiency of a car, but this must be treated as a rumour. Engine damage could still occur.
10% petrol will result in "knocking" or "pinking", where the engine runs very rough. This is because the petrol will ignite prematurely in the diesel engine, and there will be a loss of power as the combustion happens over a longer time than with 100% diesel. Some damage may also occur to the fuel supply system as petrol is less lubricative than diesel, and strips out some of the lubrication needed for diesel pumps to work well.
50% petrol will result in engine damage, as the incorrect timing of combustions will put high stresses on engine components. Something like this would happen:
100% petrol will also kill the engine. Think along the lines of these: