A Ti-based metallic glass composite with composition of Ti48Zr20Nb12Cu5Be15 exhibits good ambient plasticity in tensile and compressive loading. The macro and micro mechanisms during deformation have been investigated systematically. Obvious asymmetry between the tensile and compressive properties of the composite has been observed, indicating amorphous matrix effect on the metallic glass composite. The micro fracture mechanism of dendrites in compression can also be attributed to two mechanisms: shear induced fracture in major and tension induced fracture in local, revealing a constraint of matrix induced complex stress state in composite. Pile-ups of dislocations in dendrites cause work-hardening of composite, and the impedance of dendrites to shear bands is responsible for the improvement of plastic strain.