The cyanomethylidyne radical (CCN) has been a long-standing subject of extensive structural and spectroscopic studies. However, its chemical reactivity has received rather little attention. Recently, we studied the reaction of CCN with the simplest alkane, CH4, which follows a mechanism of carbyne insertion-dissociation rather than that of direct H abstraction proposed by a recent experimental study. However, we are aware that alkanes like CH4 bear no electron lone pairs and thus are not ideal diagnostic molecules for distinguishing between the carbyne-insertion and H-abstraction mechanisms. Hence, we chose a series of sigma-bonded molecules HX (X=OH, NH2, and F) which bear electron lone pairs and are better diagnostics for carbyne-insertion behavior. The new results at the CCSD(T)/6-311+G(2df,p)//B3LYP/6-311G(d,p)+ZPVE, CCSD(T)/aug-cc-pVTZ//B3LYP/6-311G(d,p)+ZPVE, G2M(CC1), and MC-QCISD//B3LYP/6-31G(d)+ZPVE levels definitively confirm the carbyne-insertion behavior of the CCN radical towards HX. In addition, we make the first attempt to understand the reactivity of the CCN radical toward pi-bonded molecules, using the CCN+C2H2 model reaction. This reaction involves carbenoid addition to the C[triple chemical bond]C bond without a potential-energy barrier to form a C3 three-membered cyclic intermediate followed by H extrusion. Therefore, the reactions of CCN with both sigma- and pi-bonded molecules conclusively show that CCN is a reactive carbyne radical and may be more reactive than the well-known CN radical. Future experimental studies, especially on product characterization, are strongly desired to test our proposed carbyne mechanism. The studied reactions of CCN with CH4, NH3, H2O, and C2H2 could be of interest to combustion science and astrophysics, and they could provide efficient routes to form novel cyano-containing molecules in interstellar space.