In layered transition metal dichalcogenides (LTMDCs) that display both charge density waves (CDWs) and superconductivity, the superconducting state generally emerges directly on suppression of the CDW state. Here, however, we report a different observation for pressurized TaTe2, a non-superconducting CDW-bearing LTMDC at ambient pressure. We find that a superconducting state does not occur in TaTe2 after the full suppression of its CDW state, which we observe at about 3 GPa, but, rather, a non-superconducting semimetal state is observed. At a higher pressure, ~21 GPa, where both the semimetal state and the corresponding positive magnetoresistance effect are destroyed, superconductivity finally emerges and remains present up to ~50 GPa, the high pressure limit of our measurements. Our pressure-temperature phase diagram for TaTe2 demonstrates that the CDW and the superconducting phases in TaTe2 do not directly transform one to the other, but rather are separated by a semimetal state, - the first experimental case where the CDW and superconducting states are separated by an intermediate phase in LTMDC systems.