The properties and oxidation wear patterns in the composite nanostructured coating of Zr-ZrN-(Zr,Mo,Al)N were studied during the turning of Inconel 718 alloy at the cutting speeds of vc = 125 and 200 m/min. The hardness of the coating, its elastic modulus, and critical fracture load during the scratch testing were determined. The study focused on the tribological properties of the Zr-ZrN-(Zr,Mo,Al)N coating at temperatures of 400–900 °C paired with an insert made of Inconel 718, which exhibited a certain advantage over the reference coatings of Zr-ZrN and Ti-TiN-(Ti,Cr,Al)N of similar thickness. The coating of Zr-ZrN-(Zr,Mo,Al)N provided for the longest tool life at the cutting speed of vc = 125 m/min (the tool life was four times longer in comparison with that of the uncoated tool and 15% longer in comparison with that of the Ti-TiN-(Ti,Cr,Al)N-coated tool) and at the cutting speed of vc = 200 m/min (the tool life was 2.5 times longer in comparison with that of the uncoated tool and 75% longer in comparison with that of the Ti-TiN-(Ti,Cr,Al)N-coated tool). While at the cutting speed of vc = 125 m/min, the surface coating layers exhibit only partial oxidation of the external layers (to a depth not exceeding 250 nm), with mostly preserved cubic nitride phases, and then the cutting speed of vc = 200 m/min leads to almost complete oxidation (to the depth of at least 500 nm), however, with a partially preserved nanolayered structure of the coating.