Respected Shri Adoni Suguresh,
An appointing authority is delegated with the power of appointment, in case he is the authority to issue dismissal order there certainly will be a lacunae, hence, whenever there is a dismissal, and the dismissal is a punishment, the authorised/delegated power should be used for such issuance of order. In case the same authority who is appointing a person is authorised to issue there is no other way but the order is required to be executed. These are posts carrying the power and we cannot/must not violate the sanctum of the authorities.
Let we take a simple example, if he/she is appointed to a cadre say Group-C(according to the post) with continuance of service in the time promoted to Group-B non-gazetted official, the appointing authority differ in the span, he/she is not being appointed yet, he/she did get promotion in the service, on finding prima-facie some negligence in work, the person-he/she when compelled to be dismissed the authority in fact differs, the delegated authority can execute the order and not the appointing authority on the cadre entry as group-c. In a private sector the board of directors are delegating the power, and this differs to the industry.
best of luck ...