A cryogenic composite-thin-disk amplifier with amplified spontaneous emission (ASE) rejection is implemented that overcomes traditional laser system problems in high-energy pulsed laser drivers of high average power. A small signal gain of 8 dB was compared to a 1.5 dB gain for an uncapped thin-disk without ASE mitigation under identical pumping conditions. A strict image relayed 12-pass architecture using an off-axis vacuum telescope and polarization switching extracted 100 mJ at 250 Hz in high beam quality stretched 700 ps pulses of 0.6-nm bandwidth.