The cross sections for the stripping of two correlated nucleons from light and medium-mass nuclei are considered. Such reactions are of interest both as a means for populating and identifying low-lying excited states of very exotic nuclear species and as a potential direct spectroscopic probe of two-nucleon correlations in such systems. A calculation scheme that combines the full shell model two-nucleon spectroscopic amplitudes with eikonal reaction theory is presented. The theoretical predictions of the method, and of more approximate schemes, are compared with new data on two-proton removal from $^{28}\mathrm{Mg}$. The combined full shell model structure amplitudes and reaction dynamics predictions are in good agreement with the available measurements. First indications of the sensitivity of the reaction mechanism to the spatial and angular momentum structure of the stripped two-nucleon wave functions are also discussed and clarified.