Two headrace tunnels and the drainage tunnel were excavated by tunnel boring machines (TBMs) in Jinping II Hydropower Station. During TBM excavation, two types of slabbing failure were encountered in these deep buried marble tunnels. One is rock bursting and the other is non-violent slabbing. In order to study the rock burst and slabbing failure, a unique true triaxial rock burst test was carried out to simulate the rock burst process with different in situ stresses. Four rock samples in different marble layers were obtained in the site, and then four experiments are conducted under the same stressed conditions as the in situ field. The rock burst process and slabbing failure phenomena of the four experiments are in good accordance with the observations of corresponding excavation site. The failure modes of slabbing and rock burst in different rock groups can be predicted based on the experiments. The influence of the slabbing and rock burst failure on TBM excavation is analyzed in depth. Non-violent slabbing is beneficial to the rock breakage process. Rock burst with violent slabbing process greatly affects the tunnel support, cutter and cutterhead damage, gripper movement and force and so on.