The spin degrees of freedom is crucial for the understanding of any condensed matter system. Knowledge of spin-mixing mechanisms is not only essential for successful control and manipulation of spin qubits, but also uncovers fundamental properties of investigated devices and material. For electrostatically defined bilayer graphene quantum dots, in which recent studies report spin-relaxation times T_{1} up to 50ms with strong magnetic field dependence, we study spin-blockade phenomena at charge configuration (1,2)↔(0,3). We examine the dependence of the spin-blockade leakage current on interdot tunnel coupling and on the magnitude and orientation of externally applied magnetic field. In out-of-plane magnetic field, the observed zero-field current peak could arise from finite-temperature cotunneling with the leads; though involvement of additional spin- and valley-mixing mechanisms are necessary for explaining the persistent sharp side peaks observed. In in-plane magnetic field, we observe a zero-field current dip, attributed to the competition between the spin Zeeman effect and the Kane-Mele spin-orbit interaction. Details of the line shape of this current dip, however, suggest additional underlying mechanisms are at play.