This article considers the extension of the job sequencing and tool switching problem with sequence-dependent setup times (SDSSP) and with the requirement to comply with the due date of the processed jobs. This extension is motivated by the practical application in manufacturing environment where the products manufactured may be subjected to a specific due date. This study develops a multiobjective SDSSP model (MO-SDSSP) to simultaneously minimize the total setup time of tool switches and the tardiness of the machining process. Then, a two-stage Multiobjective Adaptive Large Neighborhood Search (MOALNS) and Simulated Annealing (SA) is presented as a heuristic algorithm for the MO-SDSSP, in which the MOALNS is proposed to solve the job sequencing subproblem while the SA is used to solve the tool switching subproblem. Subsequently, the performance of MOALNS-SA is compared to several popular multiobjective optimization algorithms. Comparison on four performance criteria has shown the applicability of the MOALNS. Finally, managerial analysis is performed to analyze the relationship between the total tool setup time and the compliance of due dates.