Tungsten-copper composites are used in harsh environments because of their superior material properties. This work addresses a tungsten-copper composite made of 20 wt.% copper, which was subjected to grain refinement by high-pressure torsion, whereby the deformation temperature was varied between room temperature and 400 °C to tailor the grain size. Deformation was performed up to microstructural saturation and verified by hardness measurement and scanning electron microscopy. From the refined nanostructured material, micro-cantilever bending beams with cross-sections spanning from 5 × 5 to 35 × 35 µm ² were cut to examine possible size effects and the grain size influence on the fracture behavior. Fracture experiments were performed in situ inside a scanning electron microscope by applying a quasi-static loading protocol with partial unloading steps. Inspection of the fracture surfaces showed that all cantilevers failed in an inter-crystalline fashion. Nevertheless, remaining coarser tungsten grains impacted the resultant fracture toughness and morphology. Cantilevers fabricated from the 400 °C specimen exhibited a fracture toughness of 220 ± 50 Jm2 . For the room temperature cantilevers, a fracture toughness of 410 ± 50 Jm2 was observed, which declined to 340 ± 30 Jm2 for cantilevers < 10 × 10 µm ², confirming a size effect. The increased fracture toughness is attributed to the delamination-like structures formed in the room temperature sample.