A search for supersymmetry is presented based on events with large missing transverse energy, no isolated electron or muon, and at least three jets with one or more identified as a bottom-quark jet. A simultaneous examination is performed of the numbers of events in exclusive bins of the scalar sum of jet transverse momentum values, missing transverse energy, and bottom-quark jet multiplicity. The sample, corresponding to an integrated luminosity of 19.4 inverse femtobarns, consists of proton-proton collision data recorded at a center-of-mass energy of 8 TeV with the CMS detector at the LHC in 2012. The observed numbers of events are found to be consistent with the standard model expectation, which is evaluated with control samples in data. The results are interpreted in the context of two simplified supersymmetric scenarios in which gluino pair production is followed by the decay of each gluino to an undetected lightest supersymmetric particle and either a bottom or top quark-antiquark pair, characteristic of gluino mediated bottom- or top-squark production. Using the production cross section calculated to next-to-leading-order plus next-to-leading-logarithm accuracy, and in the limit of a massless lightest supersymmetric particle, we exclude gluinos with masses below 1170 GeV and 1020 GeV for the two scenarios, respectively.