Skyrmion-based devices are an attractive candidate for nonvolatile memory and low-power computation. In a real device, however, skyrmions easily annihilate at device edges, which hampers device applications. Here, we present a novel skyrmion-based logic device, which takes advantage of the skyrmion annihilation (SA) and increases the efficiency of logic operation. An SA half adder (HA) is implemented in a ferromagnet/heavy metal nanotrack by introducing a geometric notch that annihilates the skyrmion. In addition, full adder and n-bit SA ripple-carry adder are demonstrated by directly cascading the SA HAs. The prototype of a 32-bit SA ripple-carry adder consumes energy as low as 0.62 pJ per each operation, which is only 18% of the previously proposed skyrmion adder. Our SA logic gate can, therefore, be a promising candidate for the beyond-CMOS logic device.