Microscopic many-body theory is employed to analyze the mode-locking dynamics of a vertical external-cavity surface-emitting laser with a saturable absorber mirror. The quantum-wells are treated microscopically through the semiconductor Bloch equations and the light field using Maxwell's equations. Higher order correlation effects such as polarization dephasing and carrier relaxation at the second Born level are included and also approximated using effective rates fitted to second-Born-Markov evaluations. The theory is evaluated numerically for vertical external cavity surface emitting lasers with resonant periodic gain media. For given gain, the influence of the loss conditions on the very-short pulse generation in the range above 100 fs is analyzed. Optimized operational parameters are identified. Additionally, the fully microscopic theory at the second Born level is used to carrier out a pump-probe study of the carrier recovery in individual critical components of the VECSEL cavity such as the VECSEL chip itself and semiconductor or graphene saturable absorber mirrors.