Applying blockchain to supply chain financing is an effective way to solve the problems of financing difficulties, high financing costs, and slow financing for small and medium-sized enterprises (SMZEs). Using evolutionary game theory, this study constructs a tripartite game model and analyzes the influence of blockchain technology on the evolutionary stability strategies for financial institutions (FIs), core enterprises (CEs), and SMZEs, in which the default losses of CEs and SMZEs are assumed to be dynamic. The results of this study are as follows: (1) When CEs and SMZESs' default losses are lower than some critical value, they tend to break their promises. (2) When accounts receivable are greater than some critical value, CEs cannot repay on time because they can make a relatively large profits from delayed repayment, whereas SMZEs can be constrained to be trustworthy. Finally, the results using numerical simulation show that both relatively large default losses and enough large, trustworthy income sources can make CEs and SMZEs tend to keep their promises; in turn, CEs would be non-paying and the SMZEs tend to be trustworthy for relatively large accounts receivable. The results provide theoretical support for realizing healthy and sustainable development for supply chain finance.