Accurate extraction of mobility parameters in two-dimensional (2D) transition metal dichalcogenide (TMD)-based field-effect transistors (FETs) is crucial for evaluating their performance and optimizing device design. Conventional mobility extraction methods such as the field-effect mobility approach suffer from inaccuracies owing to the influence of series resistance and noise amplification. In this paper, we present an advanced polynomial Y-function methodology for the precise mobility characterization of MoS₂ FETs. This methodology enables a systematic discrimination among various scattering mechanisms while precisely extracting the threshold voltage. Through a comparative analysis of back-gate (BG) and top-gate (TG) MoS₂ FET configurations, we demonstrated the superior accuracy and consistency of the proposed method compared with conventional approaches. The results revealed that the TG-FET exhibited stronger surface-roughness scattering owing to the intensified transverse electric field from the thinner dielectric layer, leading to pronounced mobility degradation. The polynomial Y-function method successfully isolates key degradation factors, thereby enabling a more comprehensive understanding of the carrier transport mechanisms in 2D FETs. These findings provide a robust framework for optimizing 2D material-based electronic devices, facilitating their integration into next-generation nanoelectronic applications.