It shall be appropriate to engage the employee in process by issuing specific communications on record, reminders, and counseling and put effort on record to bring about a change.
It shall be worth to look into the reasons and address the root cause. If employee has not been like this always then who and what has caused it. This employee may be the lone employee showing the symptoms while there may be many other suffering in silence.
If yes, it shall not be good for the organization.
HR should be unbiased and should not subscribe to the tantrums of line management.
If the employee is a bad mouth, rude, arrogant, and has been like this then it is appropriate to build record and terminate. If employee can be brought on the table, shown the mirror and he offers to resign, it shall be still better.