Thermal anchor, one of the key components to keep temperature balance of gravity magnet support, should be avoided welding defects in its welding joints, which endure large forces when the international thermonuclear experimental reactor (ITER) fusion device is operating. The influences of brazing fillers and brazing methods on the cracks in joints of thermal anchor were investigated by microstructure analysis. The results have shown that the copper penetrating cracks were observed in the heat-affected zone (HAZ) of tungsten inert gas (TIG) arc brazing joints welded by CuSi3, CuSi3Mn, and Ag45CuSnNi brazing fillers, which are chiefly responsible for the diffusion and penetration of copper, derived from molten brazing filler metal into the 316L/316LN austenitic grain boundaries leading to embrittlement. The intimate contact between liquid copper and austenitic steel surface and the surface stress concentration of the austenitic steel are the main formative factors for the copper penetrating cracks. Adopting brazing fillers without containing copper or employing vacuum brazing can effectively avoid the copper penetrating cracks in the joints of ITER thermal anchor.