We demonstrated a cross-sensitivity-free torsion and strain sensor, which was achieved by using the two concatenated dispersion-turning-point (DTP)-customizable helical long-period fiber gratings (DTP-C-HLPGs). Each DTP-C-HLPG operated at the resonance wavelengths near its DTP, which could be customized by applying the vertical fiber etching technique. Thus, the radial order of the coupled cladding mode and resonance wavelengths could be flexibly adjusted as needed by changing the grating diameter. As an example, an ultrahigh sensitivity up to 2.731 nm/(rad/m) in torsion and a high sensitivity up to 0.0179 nm/ $\mu \varepsilon $ in strain was successfully achieved. Furthermore, the cross-sensitivity effect between torsion and strain could be completely eliminated by using our proposed device.