Beam structure stabilization for the high-power structured modes with transverse patterns as Lissajous figures created by an off-axis pumped degenerate-cavity laser is explored. Through the employment of a YVO4/Nd:YVO4 composite gain crystal with the front undoped segment as an effective heat spreader, it has been experimentally verified that not only the mode stability and purity of the generated Lissajous beams are significantly improved but the output power efficiency is obviously enhanced. With superior mitigation ability against the thermal aberration under high-power pumping, the proposed scheme of using the composite gain crystal to replace conventional uniformly doped crystal can offer a promising solution to realize high-power, high-order structured beams with excellent beam stability.