Conventional Transient Electromagnetic (TEM) apparent resistivity calculations typically rely on approximate formulas valid only in specific time intervals, such as the late-time approximation. As a result, their effectiveness is confined to narrow time windows, making it difficult to accurately characterize the complete subsurface resistivity structure from shallow to deep regions. Moreover, existing algorithms often assume an ideal step-off current waveform, neglecting the ramp-off effect that occurs during the actual turn-off process. This simplification can introduce blind zones and spurious high-resistivity anomalies in the early-time responses. To address these issues, this study proposes a full-space, full-time apparent resistivity calculation method for TEM that explicitly incorporates the ramp-off effect. The method is based on the canonical electric dipole response excited by an ideal step-off current, combined with precise spatial numerical integration along the actual transmitter loop to construct a forward model applicable to arbitrary observation points. A differential correction is then applied to transform the ideal response into an induced electromotive force waveform consistent with the ramp-off condition encountered in field measurements. The method iteratively fits measured data channel by channel across the entire time domain to obtain apparent resistivity values that honor the ramp-off effect in both space and time. This approach effectively eliminates distortions and false anomalies caused by neglecting the turn-off duration, thereby improving the accuracy and reliability of TEM data interpretation. Application of the method to a goaf detection case in the Ayiguozi Mine demonstrated promising results, successfully delineating multiple mined-out zones and assessing their reliability. This provides a new technical pathway for TEM surveys in geologically complex environments.