Auxetic　and　negative　thermal　expansion　metamaterials　have　a　wide　range　of　applications　in　flexible　electronics,　aerospace,　biomedicine.　Based　on　the　compression/thermal-torsion　coupling　effects,　and　combining　the　special　deformation　mechanism　of　the　planar　anti-tetrachiral　structure,　this　work　proposed　a　novel　3D　mechanical　metamaterial　with　negative　Poisson＇s　ratio　(PR)　and　negative　coefficient　of　thermal　expansion.　The　mechanical　design　method　of　the　metamaterial　is　demonstrated,　and　the　coordinated　deformation　theory　between　its　in-plane　and　out-of-plane　deformations　is　established.　By　numerical　simulation,　the　torsional　deformation　response　of　torsion　unit　of　the　metamaterials　is　explored,　and　Poisson＇s　characteristics　and　thermal　expansion　effect　of　the　metamaterials　are　analyzed.　The　results　show　that　the　PR　and　thermal　expansion　effect　of　the　metamaterial　can　be　adjusted　and　switched,　and　its　deformation　behavior　can　be　programmed.　The　coupling　design　method　for　metamaterials　provides　a　good　design　strategy　for　engineering　applications　such　as　intelligent　actuators,　flexible　robots,　and　biomedical　sensors.