Amorphous-amorphous transitions in silica glass under a variety of thermomechanical conditions are studied with molecular-dynamics simulations using a charge-transfer three-body potential model. The polyamorphic transitions can be reversible or irreversible depending on the combination of pressure and temperature at which the transitions take place. Anomalous thermomechanical behaviors of silica glass, such as an increase of the mechanical moduli upon expansion as a result of tensile deformation or thermal expansion, are well reproduced in our simulations. In part I, we show these anomalies are due to reversible structural transitions, which activate similar structural modes of displacement as in the alpha-to- beta phase transformations in cristobalite silica. The emergence of dynamic instabilities is observed in conjunction with these reversible structural changes, characterizing them as transitions rather than gradual deformations. The polyamorphic transitions are gradual and localized in silica glass in contrast to the instantaneous and extended character of polymorphic transformation in crystals. The mechanism of the irreversible transitions, the negative thermal expansion of silica glass under pressure, as well as the effect of pressure and temperature on the permanent densification of silica glass and the nature of the newly discovered amorphous phases are discussed in part II.