Nanocontainers based on solid materials have great potential for drug delivery applications. However, since nanocontainer-mediated delivery can alter the drug internalization pathways and metabolism, it is important to find out what are the mechanisms of cancer cell death induced by nanocontainers and, moreover, is it possible to regulate them. Here, we report on the detailed investigation of the internalization kinetics and intracellular spatial distribution of porous silicon nanoparticles (PSi NPs) loaded with doxorubicin (DOX) and response of cancer cells to treatment with DOX-PSi NPs as well as studies of nanocontainer biodegradation by applying various microscopy methods, Raman microspectroscopy and biological experiments with cancer cells of different etiology. The obtained results revealed the absence of toxicity of unloaded PSi NPs to cancer cells up to a concentration of 700 μg/mL during the prolonged incubation time. Thus, given the fact that the nanocontainers themselves are not toxic, it is easy to adjust the dose of the drug that they deliver to the cells. It is shown, that the treatment with DOX-loaded PSi NPs more efficiently eliminates cancer cells in comparison with the free DOX. At the same time, the obtained results demonstrate the possibility of regulating the initiation of apoptosis or necrosis in tumor cells after treatment with different concentrations of DOX-PSi NPs, as revealed by the analysis of the caspase-3 processing, the accumulation of sub-G1 cell fraction, and morphological changes determined by electron and light microscopy. The obtained results are important for future applications of porous silicon nanocontainers in drug delivery for apoptotic pathway-targeted cancer therapy.