Regardless of the dissimilarity in the crystal symmetry, the two-dimensional GaSe materials grown on GaAs(001) substrates by molecular beam epitaxy reveal a screw-dislocation-driven growth mechanism. The spiral-pyramidal structure of GaSe multi-layers was typically observed with the majority in ε-phase. Comprehensive investigations on temperature-dependent photoluminescence, Raman scattering, and X-ray diffraction indicated that the structure has been suffered an amount of strain, resulted from the screw-dislocation-driven growth mechanism as well as the stacking disorders between monolayer at the boundaries of the GaSe nanoflakes. In addition, Raman spectra under various wavelength laser excitations explored that the common ε-phase of 2D GaSe grown directly on GaAs can be transformed into the β-phase by introducing a Se-pretreatment period at the initial growth process. This work provides an understanding of molecular beam epitaxy growth of 2D materials on three-dimensional substrates and paves the way to realize future electronic and optoelectronic heterogeneous integrated technology as well as second harmonic generation applications.