Bioenergy with carbon dioxide (CO2) capture and storage (BECCS) technologies represent an interesting option to reach negative carbon emissions, which implies the removal of CO2 already emitted to the atmosphere. Chemical looping combustion (CLC) with biomass can be considered as a promising BECCS technology since CLC has low cost and energy penalty. In CLC, the oxygen needed for combustion is supplied by a solid oxygen carrier circulating between the fuel and air reactors. In the fuel reactor, the fuel is oxidized producing a CO2-concentrated stream while the oxygen carrier is reduced. In the air reactor, the oxygen carrier is regenerated with air. Chemical looping with oxygen uncoupling (CLOU) is a CLC technology that allows the combustion of solid fuels as in common combustion with air by means of an oxygen carrier that release gaseous oxygen in the fuel reactor. In the last years, several Cu-based, Mn-based, and mixed oxide oxygen (O2) carriers have been tested showing good CLOU properties. Among them, copper (Cu)-based and Cu-Manganese (Mn) mixed oxides showed high reactivity, O2 release rate, and high O2 equilibrium concentration. The aim of this work is to study the viability of biomass combustion by CLOU process. The combustion of three types of biomass (pine sawdust, olive stone, and almond shell) were studied in a continuous 1.5 kWth CLC unit. Two O2 carriers were tested: a Cu-based oxygen carrier with Magnesium, Aluminum, Oxgen (MgAl2O4) as an inert prepared by spray drying (Cu60MgAl) and a mixed Cu-Mn oxide prepared by spray granulation (Cu34Mn66). These materials are capable of releasing gaseous oxygen when they are reduced in a different range of temperatures. CO2 capture and combustion efficiency were evaluated. Two fuel reactor operation temperatures were used: 775–850 °C for Cu34Mn66 and 900–935 °C for Cu60MgAl. High CO2 capture efficiencies and 100% combustion efficiency were reached with both oxygen carriers and with all the biomasses tested. Therefore, the CLOU technology with the Cu- and Cu-Mn-based oxygen carriers allowed avoiding CO2 emissions maintaining high combustion efficiencies. Results obtained demonstrate that this innovative biomass combustion technology combined with carbon storage lets an efficient BECCS process implementation.