Some methods of asteroid hazard mitigation for the Earth using the missions to an asteroid and the control of the asteroid motion are investigated. The following methods are considered: the method of direct mechanical influence at the asteroid by the spacecraft impact and the application of a velocity impulse to the asteroid; the method of influence by a high-thrust chemical-jet engine brought onto the planet surface; the method of influence by a low-thrust electric-jet engine; the method of asteroid orbit changing by a solar sail and the method of asteroid surface painting. The characteristics of the asteroid motion control by these methods are presented. Numerical results are given for the 4179 Toutatis asteroid which flew close to the Earth in December 1992. On the basis of approximate comparative analysis of these methods the method of direct mechanical impact is chosen for the more detailed study.