As two important mechanical properties, strength and ductility generally tend to be muturally exclusive in conventional engineering materials. The breakthrough of such a trade-off has been potentiated by the recently developed CuZr-based bulk metallic glass (BMG) composites ductilized by a shape memory CuZr(B2) phase. Here the microstructural dependences of tensile properties for the CuZr-based BMG composites were elucidated qualitatively and modeled quantitatively, and the underlying mechanisms were unraveled. Through the microstructural percolation induced by matching the length scales of particle size and interparticle spacing, a notable breakthrough was achieved in the composites that the general conflicts between strength and ductility can be defeated. This study is expected to greatly aid in the microstructural design and tailoring for improved properties of BMG composites. It also has implications for the development of strong and ductile materials in the future.