We use a 1030 nm laser with 7 ps pulse duration and average power up to 100 W to ablate pyramid-shape subwavelength structures (SWS) on alumina and sapphire. The SWS give an effective and cryogenically robust anti-reflection coating in the millimeter-wave band. We demonstrate average ablation rate of up to 34 mm³/min and 20 mm³/min for structure heights of 900 μm and 750 μm on alumina and sapphire, respectively. These rates are a factor of 34 and 9 higher than reported previously on similar structures. We propose a model that relates structure height to cumulative laser fluence. The model depends on the absorption length δ, which is assumed to depend on peak fluence, and on the threshold fluence ϕ_th. Using a best-fit procedure we find an average δ = 630 nm and 650 nm, and ϕ_th = 2.0+0.5/-0.5 J/cm² and 2.3+0.1/-0.1 J/cm² for alumina and sapphire, respectively, for peak fluence values between 30 and 70 J/cm². With the best fit values, the model and data values for cumulative fluence agree to within 10\%. Given inputs for δ and ϕ_th the model is used to predict average ablation rates as a function of SWS height and average laser power.