We propose a novel scheme for frequency-tunable sub-cycle electromagnetic pulse generation. To this end a pump electron beam is injected into an electromagnetic seed pulse as the latter is reflected by a mirror. The electron beam is shown to be able to amplify the field of the seed pulse while upshifting its central frequency and reducing its number of cycles. We demonstrate the amplification by means of 1D and 2D particle-in-cell simulations. In order to explain and optimize the process, a model based on fluid theory is proposed. We estimate that using currently available electron beams and terahertz pulse sources, our scheme is able to produce mJ-strong mid-infrared sub-cycle pulses.