Type II clathrate hydrates (CHs) M-17 H2O, with M = tetrahydrofuran (THF) or 1,3-dioxolane, are known to collapse, or amorphize, on pressurization to similar to 1.3 GPa in the temperature range 77-140 K. On heating at 1 GPa, these pressure-amorphized CH states show a weak, stretched sigmoid-shaped, heat-capacity increase because of a glass transition. Here we use thermal conductivity and heat capacity measurements to show that also type II CH with M = cyclobutanone (CB) collapses on isothermal pressurization and undergoes a similar, weak, glass transition upon heating at 1 GPa. Furthermore, we reveal for both THF CH and CB CH a second, much more pronounced, glass transition at temperatures above the thermally weak glass transition on heating in the 0.2-0.7 GPa range. This result suggests the general occurrence of two glass transitions in water-rich (94 mol %) pressure-collapsed CHs. Because of a large increase in dielectric permittivity concurrently as the weak heat capacity increase, the first glass transition must be due to kinetic unfreezing of water molecules. The thermal features of the second glass transition, measured on isobaric temperature cycling, are typical of a glass liquid glass transition, which suggests that pressure-amorphized CHs transform reversibly to liquids.