The comprehensive mechanical properties of a new synthesized 3D hybrid inorganic–organic framework (TPrA)Cu2(dca)5(TPrA+= N(C3H7)4+, tetrapropylammonium; dca–= N(CN)2–, dicyanamide) have been studied via experimental approaches and first-principles calculations. The nanoindentation test demonstrates that Young’s moduli (E) and the hardness within the 2D [Cu2(dca)4] layers are respectively 65 and 70% larger than the direction normal to the 2D planes, and the framework of (TPrA)Cu2(dca)5is prone to cleavage along the 2D [Cu2(dca)4] layers to lead to discrete displacement bursts in the initial loading part of the load-indentation depth (P-h) curve of the <020> direction. The bulk modulus of (TPrA)Cu2(dca)5is 6.97 GPa within a pressure scope of 0 to 3.36 GPa, which is comparable to those from porous MIL-47 and ZIF-8. The high anisotropy of Young’s moduli of 31.8 and the shear moduli of 45.0 provided via first-principles calculations are an order of magnitude larger than those from many known porous and dense frameworks but close to those of 2D hybrid systems. The broad range of Poisson’s ratio of (TPrA)Cu2(dca)5indicates its very anisotropic response behavior when under the uniaxial and shearing stress. The results of nanoindentation, synchrotron high-pressure X-ray diffraction, and first-principles calculations synergistically indicate that the 3D architecture of (TPrA)Cu2(dca)5has the potential to cleavage into 2D nanosheets under the uniaxial or shearing stress. Further high-resolution microscopic characterization directly confirms the successful exfoliation of the 3D framework of (TPrA)Cu2(dca)5into 2D nanosheets via simple surfactant-free solvent-mediated sonication and demonstrates that the (−102) plane is the cleavage plane.