"This action would cause a constraint conflict with task #XX, 'Task Name'. Please change the date of the constraint on the successor or ensure the current task will not cause a constraint violation."
The resource you're attempting to remove is assigned to a task with a successor task with the constraint type of 'Must Start On'. Removing the resource causes a constraint violation.
Once the constraint type of the successor task of task #XX is changed to 'None', you can remove that resource from the enterprise.
You may see a lock icon on the successor task.