We show that Witt groups of spinor varieties (aka. maximal isotropic Grassmannians) can be presented by combinatorial objects called 'even shifted young diagrams'. Our method relies on the Blow-up setup of Balmer-Calmes, and we investigate the connecting homomorphism of the localization sequence via the projective bundle formula of Walter-Nenashev, the projection formula of Calmes-Hornbostel and the excess intersection formula of Fasel.