In this paper, a novel InGaZnO (IGZO) thin-film Mid-Infrared phototransistor (TF MIR PT) based on GeSn capping layer with band-gap grading (BGG) aspect is proposed and numerically investigated. Accurate numerical models are developed to study the device characteristics, where the sensor optical properties under MIR light exposure are investigated using FDTD method. Importantly, a new systematic approach based on introducing a new Figure of Merit (FoM) parameter combining noise effects, power consumption and IR photoresponse characteristics is proposed to efficiently investigate the device performance. It is found that the use of IGZO TFT platform combined with BGG GeSn sensitive layer paves the way for achieving enhanced IR photodetection characteristics, while maintaining low dark-noise effects and reduced power consumption. Moreover, it is revealed that the use of GeSn capping layer with BGG paradigm enables extended spectral sensitivity to MIR ranges, showing a high cutoff wavelength of 2.4 μm. Besides, the proposed GeSn/IGZO TF MIR PT demonstrates a giant responsivity of 550 A/W at a specific wavelength value of 1.7 μm, detectivity of 2.5 × 1014 Jones and over than 168 dB of signal-to-noise ratio. Therefore, these findings open the perspective for the design of alternative MIR sensors, offering improved photoresponse, low noise and reduced power consumption, which are highly suitable for newly emerging CMOS-compatible optical communication and optoelectronic applications.