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The high-pressure properties of the Ba-doped silicon clathrate Ba8Si46 have been investigated combining X-ray diffraction and X-ray absorption spectroscopy. A pressureinduced isostructural phase transition associated with an important volume collapse takes place at 11.5-14 GPa. This transformation is characterized by the homothetic contraction of the silicon cages containing the Ba atoms. This transition is preceded by a change in the electronic structure at 5 GPa in good agreement with Raman spectroscopy observations (T. Kume et al., Phys. Rev. Lett., 90 (2003) 155503) that it is also of isostructural nature. The cage structure is preserved through the phase transitions allowing to obtain tetrahedral silicon with record interatomic distances as low as 2.13 Å. At the highest studied pressure of 49 GPa, the structure becomes irreversibly amorphous. The physical origin of the homothetic isostructural transitions is discussed.