The efficiency of the enzyme-free toehold-mediated strand displacement (TMSD) technique is often insufficient to detect single-nucleotide polymorphism (SNP) that possesses only single base pair mismatch discrimination. Here, we report a novel dual base pair mismatch strategy enabling TMSD biosensing for SNP detection under enzyme-free conditions when coupled with catalytic hairpin assembly (CHA) and fluorescence resonance energy transfer (FRET). The strategy is based on a competitive strand displacement reaction mechanism, affected by the thermodynamic stability originating from rationally designed dual base pair mismatch, for the specific recognition of mutant-type DNA. In particular, enzyme-free nucleic acid circuits, such as CHA, emerge as a powerful method for signal amplification. Eventually, the signal transduction of this proposed biosensor was determined by FRET between streptavidin-coated 605 nm emission quantum dots (605QDs, donor) and Cy5/biotin hybridization (acceptor, from CHA) when incubated with each other. The proposed biosensor displayed high sensitivity to the mutant target (MT) with a detection concentration down to 4.3 fM and led to high discrimination factors for all types of mismatches in multiple sequence contexts. As such, the application of this proposed biosensor to investigate mechanisms of the competitive strand displacement reaction further illustrates the versatility of our dual base pair mismatch strategy, which can be utilized for the creation of a new class of biosensors.