Recently, magic-angle twisted bilayer graphene (MATBLG) has emerged with various interaction-driven novel quantum phases at the commensurate fillings of the moiré superlattice, while the charge neutrality point (CNP) remains mostly a trivial insulator. Here, we show an emerging phase of compensated semimetallicity at the CNP of twisted double bilayer graphene (TDBLG), a close cousin of MATBLG, with signatures of electronic correlation. Using electrical and thermal transport, we find two orders of magnitude enhancement of the thermopower at magnetic fields much smaller than the extreme quantum limit, accompanied by large magnetoresistance ( ~ 2500%) at CNP, providing strong experimental evidence of compensated semimetallicity at CNP of TDBLG. Moreover, at low temperatures, we observe unusual sublinear temperature dependence of resistance. A recent theory1 predicts the formation of an excitonic metal near CNP, where small electron and hole pockets co-exist. We understand this sublinear temperature dependence in terms of critical fluctuations in this theory.