The invention relates to a thin-wall part precision turning machining method and a positioning clamp, in particular to a positioning clamp and a machining method of a gyroscope motor dynamic pressure air bearing rotor cover. The positioning clamp comprises a spherical surface positioning mandrel, a positioning lantern ring, an anti-vibration pad and a back supporting seat. The spherical positioning mandrel is a step shaft with center holes formed in the two end faces, and comprises a clamping section, a large thread section, a second guide cylindrical section, a spherical positioning section, a spherical table end face, a first guide cylindrical section and a small thread section from left to right in sequence. The machining method comprises the steps of first-step machining of the rotor cover, machining of a series of spherical positioning mandrels, machining of a positioning lantern ring and a back supporting seat, selection of a proper spherical positioning mandrel, turning of the rotor cover and the like. The problems that an existing machining method is poor in positioning precision and low in machining efficiency, and the concave spherical surface is crushed are solved, damage to the concave spherical surface is avoided by limiting six degrees of freedom, and the machining precision of the rotor cover is guaranteed.