DNA methylation patterns are highly rearranged in hepatocellular carcinomas (HCCs). However, diverse sources of variation are intermingled in cancer methylomes, precluding the precise characterization of underlying molecular mechanisms. We developed a computational framework (methylation signature analysis with independent component analysis [MethICA]), leveraging independent component analysis (ICA) to disentangle the diverse processes contributing to DNA methylation changes in tumors. Applied to a collection of 738 HCCs, MethICA unraveled 13 stable methylation components (MCs) preferentially active in specific chromatin states, sequence contexts, and replication timings. These included signatures of general processes associated with gender and age but also new signatures related to specific driver events and molecular subgroups. Catenin beta 1 (CTNNB1) mutations were major modulators of methylation patterns in HCC, characterized by a targeted hypomethylation of transcription factor 7 (TCF7)‐bound enhancers in the vicinity of Wnt target genes as well as a widespread hypomethylation of late‐replicated partially methylated domains (PMDs). By contrast, demethylation of early‐replicated highly methylated domains (HMDs) was a signature of replication stress, leading to an extensive hypomethylator phenotype in cyclin (CCN)‐activated HCC. Inactivating mutations of the chromatin remodeler AT‐rich interactive domain‐containing protein 1A (ARID1A) were associated with epigenetic silencing of differentiation‐promoting transcriptional networks, also detectable in cirrhotic liver. Finally, a hypermethylation signature targeting Polycomb‐repressed chromatin domains was identified in the G1 molecular subgroup with progenitor features. Conclusion: This study elucidates the diversity of processes remodeling HCC methylomes and reveals the epigenetic and transcriptional impact of driver alterations.