Converting paper-grade bleached Kraft pulp into dissolving pulp using eco-friendly chemicals on-site at the mill is a challenge for the pulp industry. In this study, two oxidation systems are evaluated: the first one is based on the use of hydrogen peroxide at various levels of alkalinity; the second one investigates the use of sodium periodate followed by hydrogen peroxide to convert aldehydes into carboxyls and enhance their hemicelluloses removal. Our results have shown that when using only peroxide, the removal of hemicelluloses was not sufficient to improve the pulp’s dissolving ability. Conversely, the periodate–peroxide system proved to be more efficient. Results regarding the pulp purity, solubility, degradation (pulp viscosity and cellulose molecular mass distribution), brightness, and its potential applications were discussed.