The invention discloses a chip and dust removing system of a snagging machine. The chip and dust removing system comprises a gas hood, a dust absorption pipeline, a cloth bag dust collector and a fan, wherein one end of the gas hood is in an opening shape, the other end of the gas hood is communicated with one end of the dust absorption pipeline, the other end of the dust absorption pipeline is communicated with one end of the cloth bag dust collector, and the other end of the cloth bag dust collector is provided with the fan. According to the invention, a lot of dust and waste residue which are produced by the snagging machine in a grinding process can be collected by virtue of a chip absorption device and a chip removal device, thus preventing the environment from being polluted by the dust and the waste residue.