The invention concerns a method for cutting up tyres with a view to recycling them, which consists in cutting the tread (1) to separate if from the two sidewalls (2, 3) with a high pressure water jet. The invention is characterised in that the tyre is cut from the inside along a radial direction and in a liquid medium such as water. The method consists in cutting the two edges of the tread (1) so as to produce a bevel (30). The invention also concerns a method for recycling tyres in order to recover the pure rubber gum comprising a step which consists in pulverizing the bits of tyres with high pressure water jet loaded with very fine grains of an abrasive material above a vat containing a liquid, so as to obtain rubber particles with dimension not more than 12 micrometers and a step which consists in sorting out by flotation the resulting rubber particles recuperating particles free of impurities floating on the liquid and a diffusing device for implementing said method.