Though numerous studies of spin-orbit interaction (SOI) of light beams propagating along the optic axis of uniaxial crystals have been carried out, in previous studies, the initial input beams have cylindrical symmetry. In this case, the total system preserves cylindrical symmetry so that the output light after passing through the uniaxial crystal doesn't exhibit spin dependent symmetry breaking. Therefore, no spin Hall effect (SHE) occurs. In this paper, we investigate the SOI of a kind of novel structured light beam, grafted vortex beam (GVB) in uniaxial crystal. The cylindrical symmetry of the system is broken by the spatial phase structure of the GVB. As a result, a SHE determined by the spatial phase structure emerges. It is found that the SHE and evolution of the local angular momentum are controllable both by changing the grafted topological charge of the GVB and by employing linear electro-optic effect of the uniaxial crystal. This can open a new perspective to investigate the SHE of light beams in uniaxial crystals via constructing and manipulating the spatial structure of the input beams artificially, hence offers novel regulation capabilities of spin photon.