We propose a novel method to measure the time-resolved momentum distribution and size of beams with very large momentum spread. To demonstrate the principle we apply the method to the beam at the end of a Compact Linear Collider decelerator, where conventional diagnostic methods are hampered by the large energy spread of the drive beam after up to 90% of its kinetic energy is converted into microwave power. Our method is based on sweeping the beam in a circular pattern to determine the momentum distribution and recording the beam size on a screen using optical transition radiation. We present an algorithm to extract the time-resolved momentum distribution. Furthermore, the beam size along the bunch train can be extracted from the image left on a screen by sweeping the beam linearly. We introduce the analysis technique and show simulation results that allow us to estimate the applicability. In addition, we present a conceptual design of the technical realization.