The simple answer to this should be: No. A banishing ritual is typically something that is done during a Wiccan or other neopagan ritual. Its intent is to rid the area of any spirits or influences that are surrounding the sacred space so that a circle may be cast or that a summoning can begin.
From my experience this is done to appease the deities and to also ensure that the area is empty and sacred for magic or ritual. From this view, the witch or priestess is combating negative energies through a banishing ritual. A banishing is also used for ritual magic or summoning and is often referred to as ‘a license to depart’- in some occult uses. The goal is to banish the spirit or deity that was summoned or used in magic practices.
The religious use banishing rituals as well. For Christians, it is known as exorcism and also blessing. They have their ritual as well using holy water, crosses, prayer, intimidation, and expelling demons. All are intended to remove an evil influence. This is their method and it is what works for them according to their knowledge and understanding.
What all of these rituals have in common is that the person performing them assumes that there is a negative/bad/evil influence that must be removed, banished or destroyed before their god can be present, or before their magic can be cast.
Why should Satanic magicians assume that they too have to banish what is around them in order to cast spells or to perform ritual? Are they also like the Wiccans and the Christians, and other peoples of the right hand paths of paganism, religion and magic, who fear the forces around them so they must be controlled or destroyed?
For example, in the religion of Demonolatory [those who worship demons], summoning, worship and offerings are given to specific demons, and they do not use a ‘license to depart’ at the end of ritual; in fact, they use a formula of elemental invocation that creates an inner balance. From this, they invoke the demon that they are working with. This invocation of the elements, based on principles of hermetic magic is a great formula for invoking a balancing energy within.
I use their method as an example because they illustrate a necessary point about magic and ritual of the left hand path. A method of creating balance, grounding, or focusing within, is better because it creates an inner focus. This inner focus is what is necessary if you want to cast magic, or perform a ritual. Essentially you are Satanic magician who is able to balance forces within.
The image of Satanism, the pentagram, shows this idea in action in a symbolic way – the downward pointing pentagram illustrates the idea of drawing energy, strength, or spirituality from within, or from below [chthonic]. The opposite image, that points upward, symbolizes the idea of a divine spirituality from above [celestial]. These are more than just concepts about these images; it is a formula of understanding.
There are several rituals which could help to create this inner balance. From the practice of Ceremonial magic there is the Kabalistic cross of Light Ritual[Youtube Video] which is intended to be a balancing and centering meditation based on the Tree of Life and principles of kabbalism. There are also, methods of meditation, and the use of mantras for focus. The Demonolater’s methods of elemental magic invocation, as mentioned above, is interesting and perhaps useful for those of us who relate to Satan as god of this Earth. All of these methods are useful for focus, and preparation for magic.
As you can see, banishment in Satanic magic or ritual is not necessary. In fact, it is counter-productive to Satanic method in general. What is important is being able to find a method of focusing within, so that you can be prepared to manifest your will. Satanic magic was meant for the individual to practice; that is why there are no moral rules of magic that apply to Satanists as a whole.