We have used the Mambo instrument on the IRAM 30m telescope to observe at 1.2mm 63 Spitzer-selected z>1 hyperluminous infrared galaxy candidates (HLIRGs) with starburst-dominated mid-infrared (MIR) spectral energy distributions from the SWIRE Legacy survey. The primary selection criteria are a peak in the IRAC 5.8μm band due to the rest frame near-infrared spectrum of evolved stars, a bright detection at 24μm, and very faint optical counterparts. The detection rate with Mambo is very high at 45%, and both the detection rate and the average 1.2mm/24μm flux ratio are much higher than found for previous Spitzer MIR-selected samples, due to the fact that earlier samples favored systems with AGN-dominated MIR emission. Our sample, on the other hand, shows systematically lower 1.2mm/24μm ratios than a sample of Spitzer-detected submillimeter-selected galaxies (SMGs) in a similar redshift range. Thus Spitzer MIR selection complements submillimeter selection of high redshift starburst-dominated HLIRGs, finding a population with substantially different SED shapes. The large MIR/submillimeter flux ratios probably indicate exceptionally luminous 7.7μm PAH emission, based on Spitzer IRS spectra for a subset of these objects (Weedman et al. 2007).