In this paper, we investigate the response of a two-dimensional silica model glass under shear and pressure. The glass network is generated based on statistical data extracted from real two-dimensional silica. We present an amended dual bond-switching algorithm, which enables us to control both the level of heterogeneity as well as physically meaningful ring neighborhood statistics. The two-dimensionality of the model glass allows us to directly track all atoms during deformation and overcome the imaging problem of bulk silica glass. Firstly, we subject different sets of pressure-free samples to athermal quasistatic simple shear deformation. We observe a serrated flow for all levels of heterogeneity, where the stress drop statistics is described by a power law. Using the divergence theorem, it is shown that the outward flow of the local rearrangements associated with the stress drops is always higher than the inward flow, resulting in density fluctuations and nano-voids, the latter of which are detected using the shortest path criterion. However, the difference in the out-to-inward flow decreases with increasing heterogeneity. Secondly, we subject a set of one level of heterogeneity to various levels of compression, followed by athermal quasistatic shear deformation. After comparing the stress–strain results to those in bulk silica, we show that the statistics of the occurring stress drops of the densified material follow a power law. We identify an initial decrease of the out-to-inward flow with increasing pressure until a level of 10% densification followed by a slight increase up to a densification level of 15%.