Globally, huge amounts of cotton and sunflower stalks are generated annually. These wastes are being underutilized since they are mostly burned in the fields. So, in this work, we proposed a three-step method consisting of acid pre-treatment, alkaline hydrolysis, and bleaching for the extraction of cellulose pulps. These pulps were characterized to assess their morpho-structural and thermal properties. The design of experiments and response surface methodology were used for the optimization of the acid pre-treatment in order to achieve maximum removal of non-cellulosic compounds and obtain pulps enriched in cellulose. For cotton stalks, optimal conditions were identified as a reaction time of 190 min, a reaction temperature of 96.2 °C, and an acid (nitric acid) concentration of 6.3%. For sunflower stalks, the optimized time, temperature, and acid concentration were 130 min, 73.8 °C, and 8.7%, respectively. The pulps obtained after bleaching contained more than 90% cellulose. However, special care must be taken during the process, especially in the acid pre-treatment, as it causes the solubilization of a great amount of material. The characterization revealed that the extraction process led to cellulose pulps with around 69–70% crystallinity and thermal stability in the range of 340–350 °C, ready to be used for their conversion into derivatives for industrial applications.