For the first time it is experimentally demonstrated on the JET tokamak that a combination of a low impurity concentration bulk plasma and large magnetohydrodynamic instabilities is able to suppress relativistic electron beams without measurable heat loads onto the plasma facing components. Magnetohydrodynamic simulations of the instability and modeling of the postinstability plasma confirm the prompt loss of runaways and the absence of regeneration during the final current collapse. These surprising findings motivate a new approach to dissipate runaway electrons generated during tokamak plasma disruptions.