High-impact climate damages are often driven by compounding climate conditions. For example, elevated heat stress conditions can arise from a combination of high humidity and temperature. To explore future changes in compounding hazards under a range of climate scenarios and with large ensembles, climate emulators can provide light-weight, data-driven complements to Earth System Models. Yet, only a few existing emulators can jointly emulate multiple climate variables. In this study, we present the Multi-resolution EmulatoR for CompoUnd climate Risk analYsis: MERCURY. MERCURY extends multi-resolution analysis to a spatio-temporal framework for versatile emulation of multiple variables. MERCURY leverages data-driven, image compression techniques to generate emulations in a memory-efficient manner. MERCURY consists of a regional component that represents the monthly, regional response of a given variable to yearly Global Mean Temperature (GMT) using a probabilistic regression based additive model, resolving regional cross-correlations. It then adapts a reverse lifting-scheme operator to jointly spatially disaggregate regional, monthly values to grid-cell level. We demonstrate MERCURY's capabilities on representing the humid-heat metric, Wet Bulb Globe Temperature, as derived from temperature and relative humidity emulations. The emulated WBGT spatial correlations correspond well to those of ESMs and the 95% and 97.5% quantiles of WBGT distributions are well captured, with an average of 5% deviation. MERCURY's setup allows for region-specific emulations from which one can efficiently "zoom" into the grid-cell level across multiple variables by means of the reverse lifting-scheme operator. This circumvents the traditional problem of having to emulate complete, global-fields of climate data and resulting storage requirements.