An increasing number of studies have demonstrated the significant roles of the interplay between microenvironmental mechanics in tissues and biochemical-genetic activities in resident tumor cells at different stages of tumor progression. Mediated by molecular mechano-sensors or -transducers, biomechanical cues in tissue microenvironments are transmitted into the tumor cells and regulate biochemical responses and gene expression through mechanotransduction processes. However, the molecular interplay between the mechanotransduction processes and intracellular biochemical signaling pathways remains elusive. This paper reviews the recent advances in understanding the crosstalk between biomechanical cues and three critical biochemical effectors during tumor progression: calcium ions (Ca2+), yes-associated protein (YAP), and microRNAs (miRNAs). We address the molecular mechanisms underpinning the interplay between the mechanotransduction pathways and each of the three effectors. Furthermore, we discuss the functional interactions among the three effectors in the context of soft matter and mechanobiology. We conclude by proposing future directions on studying the tumor mechanobiology that can employ Ca2+, YAP, and miRNAs as novel strategies for cancer mechanotheraputics. This framework has the potential to bring insights into the development of novel next-generation cancer therapies to suppress and treat tumors.