Thermogravimetry and differential thermal analysis have been used to study the resistance to the air oxidation of high_density samples of Ti3AlC2, Ti2AlC and Ti2Al(C1–xNx) solid solutions. It has been shown that the Ti3AlC2 samples are more stable than Ti2AlC and Ti2Al(C1–xNx) solid solutions and as the nitrogen content of the solid solution increases to x = 0.75, the oxidation resistance decreases. The following characteristics have been exhibited by the material containing 89 wt % Ti3AlC2 (the rest being Al2O3 and TiC) having density 99% of theoretical: bending strength Rbm = 500 MPa, compressive strength Rcm = 700 MPa, fracture toughness KIc = 10.2 MPa⋅m0.5, hardness HRA = 70 GPa, HV = 4.6 GPa, Young modulus = 149.4 ± 28.7 GPa. After sintering with diamonds or cBN (50 wt %) at 5.5–7.7 GPa and 1350–1960°C for 0.07–1.0 h the Ti3AlC2 MAX phase decomposes to form TiC and TiAl or TiB2 and a thin layer of Al4C3 forms at the interface with diamond. The Al4C3 decomposition in a composite material due to the interaction with the air moisture results in the crack initiation along the diamond perimeter, which brings about the material fracture in 1–2 weeks. It has been found that the Ti3AlC2 powder is efficient for polishing natural and synthetic jewelry crystals and competitive in polishing efficiency and quality with ACM 2/1 grade diamond.