A method for drilling or cutting a pin surrounded by solid material includes the use of a water jet tool having a nozzle that is arranged at an angle with respect to a main body of the water jet tool. The water jet is directed over a portion of the surface of the pin, and removes that portion thereby fragmenting the pin. In order to minimize damage to the surrounding material, the portions removed touches the interface between the pin and the surrounding solid material at a minimal number of points and over a minimal extent of the interface. The method is applicable in particular to the removal of pins used in a press-fit for the securing of blades on a turbine rotor. The method facilitates “in situ” removal of pins within a confined space in a short time and at reduced cost.