Currently, the surface acoustic wave (SAW) magnetic field sensing technique utilises the SAW velocity/frequency mechanism of magnetoacoustic interaction as an indicator of the magnetic sensitivity mechanism. However, this method has low sensitivity and poor stability. To address this problem, a dynamic magnetoelastic coupling theoretical model is constructed to theoretically simulate the influence of the ∆E effect of magnetically sensitive thin films on SAW propagation attenuation. This study describes a high-sensitivity SAW magnetic field sensing mechanism based on magnetoacoustic attenuation. The simulation results show a clear relationship between the acoustic propagation loss and external magnetic field, indicating a structure-property relationship. An amorphous soft magnetic material (Fe90Co10)78Si12B10 was used as a magnetically sensitive thin film due to its high permeability, low coercivity (Hc), low hysteresis, ease of magnetisation and demagnetisation. SAW magnetosensitive device operating on a frequency of 200 MHz has been experimentally developed using a standard semiconductor photolithography process. A SiO2 layer was deposited on a 36° YX-LiTaO3 substrate as a waveguide, and a (Fe90Co10)78Si12B10 layer was on the top of the propagation area as a magnetosensitive film. The experimental results showed that the acoustic loss change due to the magnetic field variation was 4.63 dB within a magnetic field range of 0 Oe to ±10 Oe, which agreed with the theoretical results. The sensor had a sensitivity of 0.7546 dB/Oe within the range of 0 to 4 Oe and the lower detection limit of magnetic fields was 0.272 Oe, low hysteresis error of 0.54%, multiple repeatability error of 0.13%, excellent repeatability and stability were achieved in the experiments from the developed sensing device.