We have prepared amorphous clathrate hydrates of Ar, CD4, Xe, and SF6 by depositing mixed vapors of water and guest molecules on a substrate at ca. 10 K. The structure and vibrational density of states were investigated by neutron diffraction and inelastic scattering techniques, respectively. The radial distribution functions of the amorphous hydrates are larger than that of pure amorphous ice in the region around 4 angstrom (the center-edge distance of the 12-hedral cage), indicating that a local cagelike structure is maintained even in the amorphous solids. The incorporation of the guest molecules decreases the intensity of the phonon excitation below 7 meV, which is known as a low-energy excitation characteristic of amorphous ice. This may be due to the effect that the disorder, defects and distortion producing the low-energy excitation are reduced by a hydrophobic hydration between the guest and water molecules and the resultant hydrogen-bond formation. A similar effect was also observed in the libration mode of water molecules at about 60 meV. The present work has revealed the relation among the local cage formation, hydrogen bonds, and low energy excitations in amorphous hydrates that is the simplest hydrophobic hydration system (H2O-gas mixture).