The ALMA Survey of 70 µm dark High-mass clumps in Early Stages (ASHES) has been designed to systematically characterize the earliest stages and to constrain theories of high-mass star formation. A deep understanding of highmass star formation requires the study of the clustered mode, which is the most commonly found in nature. A total of 12 massive (>500 M ), cold (≤15 K), 3.6-70 µm dark prestellar clump candidates, embedded in infrared dark clouds (IRDCs), were carefully selected in the pilot survey to be observed with the Atacama Large Millimeter/sub-millimeter Array (ALMA). Exploiting the unique capabilities of ALMA, we have mosaiced each clump (∼1 arcmin 2 ) in dust continuum and line emission with the 12 m, 7 m, and Total Power arrays at 224 GHz (1.34 mm), resulting in ∼1. 2 angular resolution (∼4800 AU at the average source distance of 4 kpc). As the first paper of the series, we concentrate on the dust continuum emission to reveal the clump fragmentation. We have detected a total of 294 cores, from which 84 (29%) are categorized as protostellar based on outflow activity or "warm core" line emission. The remaining 210 (71%) are considered prestellar core candidates. The number of detected cores is independent of the mass sensitivity range of the observations and, on average, more massive clumps tend to form more cores. We find no correlation between the mass of the host clump and the most massive embedded core. We find a large population of low-mass (<1 M ) cores and no high-mass (>30 M ) prestellar cores. The most massive prestellar core has a mass of 11 M . From the prestellar core mass function, we derive a power law index of 1.17 ± 0.10, slightly shallower than the Salpeter index of 1.35. We have used the minimum spanning tree technique to characterize the separation between cores and their spatial distribution, and to derive mass segregation ratios. While there is a range of core masses and core separations detected in the sample, the mean separation and mean mass of cores per clump are well explained