Heat shock protein 70 (Hsp70s) family members are present in virtually all living organisms and perform a fundamental role against different types of environmental stressors and pathogenic organisms. Marine bivalves live in highly dynamic environments and may accumulate paralytic shellfish toxins (PSTs), a class of well-known neurotoxins closely associated with harmful algal blooms (HABs). Here, we provide a systematic analysis of Hsp70 genes (PyHsp70s) in the genome of Yesso scallop (Patinopecten yessoensis), an important aquaculture species in China, through in silico analysis using transcriptome and genome databases. Phylogenetic analyses indicated extensive expansion of Hsp70 genes from the Hspa12 sub-family in the Yesso scallop and also the bivalve lineages, with gene duplication events before or after the split between the Yesso scallop and the Pacific oyster. In addition, we determined the expression patterns of PyHsp70s after exposure to Alexandrium catenella, the dinoflagellate producing PSTs. Our results confirmed the inducible expression patterns of PyHsp70s under PSTs stress, and the responses to the toxic stress may have arisen through the adaptive recruitment of tandem duplication of Hsp70 genes. These findings provide a thorough overview of the evolution and modification of the Hsp70 family, which will gain insights into the functional characteristics of scallop Hsp70 genes in response to different stresses.