A multidimensional model is adopted to investigate the combustion and emission formation of a dimethyl ether (DME) and methanol dual-fuel homogeneous charge compression ignition engine. The multidimensional model couples with a reduced chemical mechanism so that the heat transfer and in-cylinder turbulence are considered in the combustion modeling. The results show that the calculated results agree well with the experimental results. Both low- and high-temperature reactions take place in some specific locations in the cylinder and then propagate to the entire cylinder. The quasi-low-temperature reaction occurs in the core zone first, and the high-temperature reaction starts from the core zone adjacent to the combustion chamber axis. The main compositions of unburned hydrocarbon (UHC) emissions are the unburned fuels (DME and methanol) and CH2O. The unburned fuels mainly reside in the piston-ring crevice region, and CH2O is mainly from the region next to the cylinder-liner wall. The majority of CO emissions are located in the region near the top surface of the piston. With the increase of the total fuel/air equivalence ratio or the DME proportion, UHC and CO emissions decrease. However, when the total fuel/air equivalence ratio or the DME proportion is too small, CO emissions decrease too. When the maximum average temperature in the cylinder is over 1400 K, both UHC and CO emissions are very low.