断绝 (duàn jué) means to sever or break off relations, ties, or connections — it implies a complete and often permanent end to a relationship or link. It is more formal and absolute than 中断 (zhōng duàn, to interrupt a process) or 中止 (zhōng zhǐ, to suspend/cease an activity), and is used specifically for abstract connections (关系, 联系) rather than physical objects.