The invention relates to a drilling device suitable for a high-strength oblique rock surface in a narrow space. The drilling device comprises a percussion reverse circulation drill, a steel mud tank,a mud and sand separator, an isolation board, steel casings and a communication pipe. A construction method comprises the steps: 1, the percussion reverse circulation drill is adopted in the drillingprocess of a drilled pile; 2, the steel mud tank is configured near a hole site, and the mud tank is provided with isolation compartments through the isolation board; 3, the mud and sand separator ismounted in the steel mud tank, and separated drilling residue enters the isolation compartments of the mud tank; 4, mud flows into the adjacent steel casings to be further precipitated; and 5, the communication pipe is mounted to enable the precipitated mud to flow into a hole, and the mud is circularly constructed. The drilling device has the advantages that arrangement of the steel mud tank takes the place of arrangement of a precious large mud pool, the steel mud tank can be independently placed near a pile site, the mud circulating effect is obvious, residue specimens are convenient to remain and are transported to a designated discharging place easily, meanwhile the structure is concise, operation is convenient, the construction speed is high, and thus the construction progress and quality of the drilled pile and environmental protection are effectively controlled.