We analyze the nonlinear dynamics of a semiconductor laser with optical injection from a frequency comb. When varying both the injection parameters (detuning and injection ratio) and the comb properties (number of comb lines and comb spacing), we identify and select several dynamics, including (1) injection locking with selective amplification of the comb line that shows the smallest detuning from the injected laser, (2) unlocked time-periodic dynamics that correspond to a new frequency comb with a broadened optical spectrum, thereby sharpening the pulse generated at the injected laser output, and (3) unlocked chaotic dynamics.