Metamaterials with multimodal deformation mechanisms resemble machines1,2, especially when endowed with autonomous functionality. A representative architected assembly, with tunable chirality, converts linear motion into rotation3. These chiral metamaterials with a machine-like dual modality have potential use in areas such as wave manipulation4, optical activity related to circular polarization5 and chiral active fluids6. However, the dual motions are essentially coupled and cannot be independently controlled. Moreover, they are restricted to small deformation, that is, strain ≤2%, which limits their applications. Here we establish modular chiral metamaterials, consisting of auxetic planar tessellations and origami-inspired columnar arrays, with decoupled actuation. Under single-degree-of-freedom actuation, the assembly twists between 0\textdegree and 90\textdegree, contracts in-plane up to 25% and shrinks out-of-plane more than 50%. Using experiments and simulations, we show that the deformation of the assembly involves in-plane twist and contraction dominated by the rotating-square tessellations and out-of-plane shrinkage dominated by the tubular Kresling origami arrays. Moreover, we demonstrate two distinct actuation conditions: twist with free translation and linear displacement with free rotation. Our metamaterial is built on a highly modular assembly, which enables reprogrammable instability, local chirality control, tunable loading capacity and scalability. Our concept provides routes towards multimodal, multistable and reprogrammable machines, with applications in robotic transformers, thermoregulation, mechanical memories in hysteresis loops, non-commutative state transition and plug-and-play functional assemblies for energy absorption and information encryption.