10 kV silicon carbide (SiC) MOSFETs have been receiving increasing research attention in medium voltage (MV) applications. Compared with silicon (Si) IGBT counterparts, 10 kV SiC MOSFETs exhibit shorter short-circuit withstand time (SCWT), which requires fast and reliable short-circuit protection (SCP) circuits. The di/dt-based SCP circuit is a promising solution because of its fast response and simple implementation without additional current sensors. However, a major limitation of the di/dt-based method is its inability to detect the dc component of the current, resulting in prolonged detection time during a fault-under-load (FUL) event. This paper proposes a novel di/dt-based SCP circuit with decoupled SCP thresholds for hard-switching-fault (HSF) and FUL of 10 kV SiC MOSFETs. The proposed circuit differentiates HSF and FUL states by monitoring the gate voltage and automatically adjusts the SCP threshold voltage for FUL, thereby accelerating short-circuit (SC) detection for FUL events. In addition, a simple constant-current soft-turn-off (STO) circuit is proposed to minimize the SC turn-off overvoltage. Experimental results with a 10 kV SiC MOSFET module verified the effectiveness of the proposed circuits.