High-power, high-purity, nanosecond (ns) one-dimensional HG0n laser beams are proposed and demonstrated by using Nd:YAG cascaded slabs with a large aspect ratio. The HG0n laser beams are generated by adjusting the pump distribution, the intracavity apertures, and the tilt angle of the output coupler (OC). By controlling the gain and loss of HG0n modes of different orders, the high-purity, one-dimensional, high-order HG0n laser beams with orders 1 to 9 (HG01 to HG09) are produced, and their beam quality factors M2 align well with the theoretical predictions. Meanwhile, the large aspect ratio slab provides an ideal amplifier for the strip-shaped HG0n laser beams, and further power scaling is achieved by seeding the generated HG0n laser beams into an amplifier with an identical slab module. For the HG09 mode, the average power is amplified from 289 mW to 4.73 W with 294 ns pulse width, corresponding to a peak power of 32 kW. Moreover, above 5 W average power is achieved for all HG01 to HG08 modes. Hopefully, this scheme provides a solution for high-power and high-purity HG0n laser beam generation based on the slab-shaped configuration.