I suggest you use morph target animation for this use case. In Blender they are called Shape Keys. You can then export to glTF and import via THREE.GLTFLoader. The twist can be controlled by modulating Mesh.morphTargetInfluences. It's even possible to animate a transition from on state of the mesh to another.
Note that loop cuts do not exist as an entity if you export a mesh from Blender to e.g. glTF. It is of course possible to change the geometry in three.js as you like but using morph targets seems the easier approach. Especially for a beginner in three.js or computer graphics in general.
three.js R113