Flexible and multifunctional strain sensors with superior properties including high sensitivity, low detection limits, and a wide sensing range are always in high demand for wearable electronics. However, it remains a big challenge to fully satisfy the aforementioned requirements. In particular, there is always a trade-off between high sensitivity and wide sensing range. Here, we developed a multifunctional strain sensor based on a network-structured MXene/polyurethane mat (network-M/P mat) and well balanced the relationship between the sensitivity and sensing range by rationally designing the morphology and microstructures of the sensing device. The network-structured polyurethane mat (network-P mat) was fabricated through a facile and scalable electrospinning technique. The highly conductive MXene sheets were decorated onto the network-P mat through hydrogen bonding or electrostatic interactions. The obtained highly flexible and stretchable network-M/P mat exhibited a superior comprehensive sensing performance that was characterized by high sensitivity (gauge factor up to 228), a low limit of detection (0.1%), a large and tunable sensing range (up to 150%), excellent stability (over 3200 cycles), and multiple functions (lateral strain, vertical pressure, bending and subtle vibration). Based on its superior performance, the network-M/P mat-based strain sensor can detect a full range of body actions and subtle physiological signals (e.g. respirations and pulse waves), demonstrating great potential for applications in artificial electronic skin and wearable health detectors.