We describe the production and verification of sky maps of the five Spectral and Photometric Imaging Receiver (SPIRE) fields observed as part of the Herschel Multi-tiered Extragalactic Survey (HerMES) during the Science Demonstration Phase (SDP) of the Herschel mission. We have implemented an iterative map-making algorithm [The SPIRE-HerMES Iterative Mapper (SHIM)] to produce high fidelity maps that preserve extended diffuse emission on the sky while exploiting the repeated observations of the same region of the sky with many detectors in multiple scan directions to minimize residual instrument noise. We specify here the SHIM algorithm and outline the various tests that were performed to determine and characterize the quality of the maps and verify that the astrometry, point source flux and power on all relevant angular scales meet the needs of the HerMES science goals. These include multiple jackknife tests, determination of the map transfer function and detailed examination of the power spectra of both sky and jackknife maps. The map transfer function is approximately unity on scales from 1 arcmin to 1°. Final maps (v1.0), including multiple jackknives, as well as the SHIM pipeline, have been used by the HerMES team for the production of SDP papers.