Recent studies have made remarkable progress in histopathology classification. Based on current successes, contemporary works proposed to further upgrade the model towards a more generalizable and robust direction through incrementally learning from the sequentially delivered domains. Unlike previous parameter isolation based approaches that usually demand massive computation resources during model updating, we present a memory-efficient prompt tuning framework to cultivate model generalization potential in economical memory cost. For each incoming domain, we reuse the existing parameters of the initial classification model and attach lightweight trainable prompts into it for customized tuning. Considering the domain heterogeneity, we perform decoupled prompt tuning, where we adopt a domain-specific prompt for each domain to independently investigate its distinctive characteristics, and one domain-invariant prompt shared across all domains to continually explore the common content embedding throughout time. All domain-specific prompts will be appended to the prompt bank and isolated from further changes to prevent forgetting the distinctive features of early-seen domains. While the domain-invariant prompt will be passed on and iteratively evolve by style-augmented prompt refining to improve model generalization capability over time. In specific, we construct a graph with existing prompts and build a style-augmented graph attention network to guide the domain-invariant prompt exploring the overlapped latent embedding among all delivered domains for more domain-generic representations. We have extensively evaluated our framework with two histopathology tasks, i.e., breast cancer metastasis classification and epithelium-stroma tissue classification, where our approach yielded superior performance and memory efficiency over the competing methods.