An icosahedral Al-Pd-Mn quasicrystal sample is laser vaporized to form metal clusters by gas aggregation. The clusters are subsequently laser ionized and mass analyzed in a time-of-flight mass spectrometer. The mass spectra show cluster compositions which are qualitatively similar to that of the sample. This is consistent with a kinetically controlled cluster growth process. Cluster thermodynamic stability is probed by multiphoton ionization/fragmentation, which induces primarily Al and Mn loss. The resulting spectra are composed of a series of Pd-rich Al-Pd clusters. The average cluster composition is 60 (+/-1)% Pd. This composition is close to a known eutectic in the Al-Pd system. When manganese is seen on these clusters, it is always in units of Mn-3. These results are discussed in terms of relative binding strengths in the Al-Pd-Mn alloy system.