For explaining the AMS-02 cosmic positron excess, which was recently reported, we consider a scenario of thermally produced and decaying dark matter (DM) into the standard model (SM) leptons with an extremely small decay rate, ΓDM∼10−26  sec−1. Since the needed DM mass is relatively heavy (700  GeV≲mDM≲3000  GeV), we introduce another DM component apart from the lightest supersymmetric particle (LSP). For its (meta-)stability and annihilation into other particles, the new DM should be accompanied with another Z2 symmetry apart from the R parity. Sizable renormalizable couplings of the new DM with SM particles, which are necessary for its thermalization in the early universe, cannot destabilize the new DM because of the new Z2 symmetry. Since the new DM was thermally produced, it can naturally explain the present energy density of the Universe. The new DM can decay into the SM leptons (and the lightest supersymmetric particle) only through nonrenormalizable operators suppressed by a superheavy squared mass parameter after the new Z2 symmetry is broken around TeV scale. We realize this scenario in a model of “gauged vectorlike leptons,” which was proposed recently for the naturalness of the Higgs boson.