Topological materials exhibit topologically protected surface states (TSS) characterized by helical spin texture and high charge-spin conversion efficiency, making them promising for high-performance spintronic devices. However, achieving gate control to switch between up and down spin-polarized states of TSS has been a significant challenge for developing spin field-effect transistors (FETs). Additionally, the limited density of states of TSS restricts the on-state spin signals and, consequently, the spin on-off ratio. Here, we demonstrate gate-tunable spin textures in the topological semimetal Cd_{3}As_{2} achieved through surface modification with gold atoms, which induces the Rashba spin-splitting states (RSS) alongside the intrinsic TSS. The dominant spin textures are modulated by gate voltages, enabling the realization of spin-polarized current FETs. The incorporation of RSS enhances spin polarization signals, particularly in the conduction band, resulting in a gate-tunable on-off ratio of 72 000%, and exhibiting a highly efficient field-effect spin switching. Moreover, the emergent RSS generate a significant bilinear magnetoelectric resistance, which reverses its sign from the electron to hole regime. Our Letter presents a promising surface engineering approach for implementing spin FETs in topological materials, paving the way for advancements in spintronics.