The present invention discloses an assembly and a method for controllably decomposing waste through incineration. The assembly comprises an oxyhydrogen generating unit for generating an oxyhydrogen gas, a portable incinerator for combusting a waste material feedstock received therein using the oxyhydrogen gas, a power supplying unit comprising an output converter coupled to a plurality of energy sources for providing an electrical power to the said oxyhydrogen generating unit, a power control unit comprising a current control circuit for selectively establishing a voltage level and a current level of the said electrical power from the power supplying unit to feed into the oxyhydrogen generating unit based on an adaptive current limitation responsive to a first temperature and a second temperature respectively corresponding to temperatures of the oxyhydrogen generating unit and the portable incinerator, and a pulse width modulation generator electrically connected with the power control unit for generating a modulation signal corresponding to the adaptive current limitation to proportionally trigger the output converter thereof. The power control unit reduces the adaptive current limitation when any one of the first temperature and the second temperature exceeds a predetermined temperature threshold.