A combined experimental and analytical approach is undertaken to identify the relationship between process parameters and fracture behavior in the cutting of a 1mm thick alumina samples by a hybrid CO2 laser∕waterjet (LWJ) manufacturing process. In LWJ machining, a 200W power laser was used for local heating followed by waterjet quenching of the sample surface leading to thermal shock fracture in the heated zone. Experimental results indicate three characteristic fracture responses: scribing, controlled separation, and uncontrolled fracture. A Green’s function based approach is used to develop an analytical solution for temperatures and stress fields generated in the workpiece during laser heating and subsequent waterjet quenching along the machining path. Temperature distribution was experimentally measured using thermocouples and compared with analytical predictions in order to validate the model assumptions. Computed thermal stress fields are utilized to determine the stress intensity factor and energy release rate for different configurations of cracks that caused scribing or separation of the workpiece. Calculated crack driving forces are compared with fracture toughness and critical energy release rates to predict the equilibrium crack length for scribed samples and the process parameters associated with transition from scribing to separation. Both of these predictions are in good agreement with experimental observations. An empirical parameter is developed to identify the transition from controlled separation to uncontrolled cracking because the equilibrium crack length based analysis is unable to predict this transition. Finally, the analytical model and empirical parameter are utilized to create a map that relates the process parameters to the fracture behavior of alumina samples.