In the context of chemical recycling of mixed plastics and paper, multitemperature step pyrolysis has shown good potential for the separation of oxygenated products from hydrocarbons. Here, we report results of an investigation of the first pyrolysis step at low temperature, which involves the dehydrochlorination of polyvinyl chloride (PVC) and the pyrolysis of cellulose, the main component of paper. Calcium oxide (CaO), selected for its chloride adsorption ability and its catalytic activity on biooil deoxygenation, was used for upgrading the downstream products from the pyrolysis. Additionally, we studied the performance of CaO for the simultaneous adsorption of HCl and for reforming cellulose pyrolysates in the temperature range of 300–600 °C with feedstock to CaO ratios of 1:0.2, 1:0.4, and 1:1. It was found that the suitable catalytic temperature for HCl and acetic acid adsorption is lower than 400 °C. This is due to the desorption of HCl from CaCl2 and Ca(OH)Cl in the presence of water and CO2 at 400 °C and higher. A larger amount of CaO resulted in a more efficient reduction of acids and the organic liquids were found to have lower amounts of oxygen. A comparison between the cases of neat and mixed feedstock showed that pyrolysis of mixed feedstock produced more water, H2, CO, and polycyclic aromatic hydrocarbons (PAHs) when compared to the case of neat materials over CaO.