首先，构建id/部门组合存在多少次的Map。
然后删除计数大于1的所有条目。
例子

List<EmpData> data = List.of();

TreeMap<EmpData, Long> counts = data.stream().collect(Collectors.groupingBy(
        Function.identity(),
        () -> new TreeMap<>(Comparator.comparing(EmpData::getId)
                                  .thenComparing(EmpData::getDepartment)),
        Collectors.counting()));
data.removeIf(e -> counts.get(e) > 1);

您可以对其进行排序，然后删除所有后续的：

var sorted = list.stream().sort(Comparator.comparing(EmpData::getId).thenComparing(EmpData::getDepartment)).collect(Collectors.toList());

for(int i = 0; i < sorted.size() - 1; i++){
   var next = sorted.at( i + 1 );
   var current = sorted.at( i );
   if(current.getId().equals(next.getId()) && current.getDepartment().equals(next.getDepartment())){
      sorted.remove(i);
      i--; // check for next element
   }
}

data.stream().distinct().collect(Collectors.toList());