Yne-diamond -a new carbon allotrope constructed by inserting two carbon atoms into the carbon-carbon bonds of diamond was expected to have super-hardness comparable to diamond because of the three-dimensional network of strong sp-sp(3) and sp-sp bonds. However, from a theoretical point of view, this idea has never been validated carefully. Based on first-principles calculations, we present the first theoretical evidence that, in contrast to the early expectation, yne-diamond possesses low ideal tensile strength, low shear strength and small Pugh's modulus ratio, owning to the large void network in the covalent bond skeleton. Combined with a simple model, we predict that the yne-diamond family will not be a super-hard material family. This provides a new understanding of the mechanical properties of carbon allotropes containing sp-hybridized carbon atoms.