Surface-acoustic-wave- (SAW) based devices emerge as promising technology in magnetic field sensing by integrating a magnetostrictive layer with the giant \ensuremath{\Delta}E/\ensuremath{\Delta}G effect. However, almost all SAW magnetic field sensors require a bias field to obtain high sensitivity. In addition, the true nature of magnetoacoustic coupling still presents a major challenge in understanding and designing this kind of device. Here, a dynamic magnetoelastic model for the \ensuremath{\Delta}E/\ensuremath{\Delta}G effect is established in consideration of the important role of the dipole-dipole interaction. The model is also implemented in finite-element-method software to calculate the resonance-frequency responses of multiple fabricated sensors with different \ensuremath{\psi} angles between the acoustic wave vector and the induced uniaxial magnetic anisotropy. The measured results are in excellent agreement with the simulated ones. A strong resonance-frequency sensitivity (${S}_{\mathrm{RF}}$) of 630.4 kHz/Oe is achieved at zero bias field for the device with an optimized \ensuremath{\psi} angle. Furthermore, the ${S}_{\mathrm{RF}}$ measurements along different directions verify its vector-sensing capability.