The mechanism for the amorphization induced by mechanical alloying has been studied in the immiscible Cu-Ta system characterized by a positive heat of mixing of 2kJ/㏖. Here a chemical driving force is no longer expected and instead an energetically up-hill process has been proposed for the formation of the amorphous phase. From the studies on the atomic-level structure through the neutron diffraction and extended X-ray absorption fine structure coupled with thermodynamical consideration, we provide various evidences for the amorphization due to mechanical alloying for a mixture of Cu and Ta powders, The coordination number around Cu and Ta atoms is deduced by assuming the first neighbors of the total pair distribution function g(r) to consist of the three partial ones. We conclude that the amorphization proceeds such that the smaller Cu atoms preferentially enter into the bcc Ta lattice and destroy the long range order edtructure of a crystalline phase.