We report a field-temperature phase diagram and an entropy map for the heavy-fermion compound CeAuSb2. CeAuSb2 orders antiferromagnetically below TN=6.6 K and has two metamagnetic transitions, at 2.8 and 5.6 T. The locations of the critical end points of the metamagnetic transitions, which may play a strong role in the putative quantum criticality of CeAuSb2 and related compounds, are identified. The entropy map reveals an apparent entropy balance with Fermi-liquid behavior, implying that above the Néel transition the Ce moments are incorporated into the Fermi liquid. High-field data showing that the magnetic behavior is remarkably anisotropic are also reported.