We present a dynamically tunable mechanism of wave transmission in one-dimensional helicoidal phononic crystals in a shape similar to DNA structures. These helicoidal architectures allow slanted nonlinear contact among cylindrical constituents, and the relative torsional movements can dynamically tune the contact stiffness between neighboring cylinders. This results in cross-talking between in-plane torsional and out-of-plane longitudinal waves. We numerically demonstrate their versatile wave mixing and controllable dispersion behavior in both wavenumber and frequency domains. Based on this principle, a suggestion toward an acoustic configuration bearing parallels to a transistor is further proposed, in which longitudinal waves can be switched on and off through torsional waves.