There is a growing appreciation that mutagenic processes can be studied through the lenses of mutational signatures – characteristic mutation patterns attributed to individual mutagens. However, the link between mutagens and observed mutation patterns is not always obvious. While some mutation signatures have been connected to specific causes such as UV light exposure, smoking, or other biochemical processes, elucidating the causes of many signatures, especially those associated with endogenous processes, remains challenging. In addition, endogenous mutational processes interact with each other, as well as with other cellular processes, in ways that are not fully understood.To gain insights into the relations between mutational signatures and cellular processes, we developed a network-based approach termed GeneSigNet. The main idea behind the approach is to utilize gene expression and signature activities for the construction of a directed network containing two types of nodes corresponding to genes and signatures respectively. The construction utilizes a sparse partial correlation technique complemented with a higher moment-based approach assigning edge directionality when possible.Application of the GeneSigNet approach to breast and lung cancer data sets allowed us to capture a multitude of important relations between mutation signatures and cellular processes. In particular, the model suggests a causative influence of the homologous recombination deficiency signature (SBS3) on a clustered APOBEC mutation signature and linked SBS8 with the NER pathway. Interestingly, our model also uncovered a relation between APOBEC hypermutation and activation of regulatory T Cells (Tregs) known to be relevant for immunotherapy, and a relation between the APOBEC enzyme activity (SBS2) and DNA conformation changes. GeneSigNet is freely available at https://github.com/ncbi/GeneSigNet.