We present the results of a new spectroscopic survey for dusty intervening absorption systems, particularly damped Lyα absorbers (DLAs), toward reddened quasars. The candidate quasars are selected from mid-infrared photometry from the Wide-field Infrared Survey Explorer combined with optical and near-infrared photometry. Out of 1073 candidates, we secure low-resolution spectra for 108 using the Nordic Optical Telescope on La Palma, Spain. Based on the spectra, we are able to classify 100 of the 108 targets as quasars. A large fraction (50%) is observed to have broad absorption lines (BALs). Moreover, we find six quasars with strange breaks in their spectra, which are not consistent with regular dust reddening. Using template fitting, we infer the amount of reddening along each line of sight ranging from A(V) ≈ 0.1 to 1.2 mag (assuming a Small Magellanic Cloud extinction curve). In four cases, the reddening is consistent with dust exhibiting the 2175 Å feature caused by an intervening absorber, and for two of these, an Mg ii absorption system is observed at the best-fit absorption redshift. In the rest of the cases, the reddening is most likely intrinsic to the quasar. We observe no evidence for dusty DLAs in this survey. However, the large fraction of BAL quasars hampers the detection of absorption systems. Out of the 50 non-BAL quasars, only 28 have sufficiently high redshift to detect Lyα in absorption.