The mechanisms leading to the development and progression of hepatocellular carcinoma (HCC) are complicated and regulated genetically and epigenetically. The recent advancement in high-throughput sequencing has facilitated investigations into the role of genetic and epigenetic regulations in hepatocarcinogenesis. Therefore, we used systems biology and big database mining to construct genetic and epigenetic networks (GENs) using the information about mRNA, miRNA, and methylation profiles of HCC patients. Our approach involves analyzing gene regulatory networks (GRNs), protein-protein networks (PPINs), and epigenetic networks at different stages of hepatocarcinogenesis. The core GENs, influencing each stage of HCC, were extracted via principal network projection (PNP). The pathways during different stages of HCC were compared. We observed that extracellular signals were further transduced to transcription factors (TFs), resulting in the aberrant regulation of their target genes, in turn inducing mechanisms that are responsible for HCC progression, including cell proliferation, anti-apoptosis, aberrant cell cycle, cell survival, and metastasis. We also selected potential multiple drugs specific to prominent epigenetic network markers of each stage of HCC: lestaurtinib, dinaciclib, and perifosine against the NTRK2, MYC, and AKT1 markers influencing HCC progression from stage I to stage II; celecoxib, axitinib, and vinblastine against the DDIT3, PDGFB, and JUN markers influencing HCC progression from stage II to stage III; and atiprimod, celastrol, and bortezomib against STAT3, IL1B, and NFKB1 markers influencing HCC progression from stage III to stage IV.