A similarly named ability also appears as a recurring earth-elemental spell in Final Fantasy XI and Final Fantasy XIV. However, this ability is considered separate from the recurring MP damaging spell, which is known as "Raspir" in Japanese.
Damages the target's MP.Description
Rasp is an effect spell that is taught by Zona Seeker at a x20 rate and Shiva at a x4 rate. It deals damage to the target's MP at the cost of 12 MP. It has a Power of 10, Hit rate of 150, and is vulnerable to Runic. There are many enemies that can be killed by bringing their MP down to 0. Skull Dragon when fought against in the Dragons' Den can only be defeated with Rasp.
Deals damage to MP.Description
Alchemists and Templars can cast Rasp for 24 MP, and is learned from the Apocalypse for the Templar for 100 AP, and the Energy Mace for the Alchemist for 100 AP. It has a Magic Power of 60, a range of 3, is stealable through the Steal: Ability, and is also susceptible to Return Magic. It deals damage to MP.
Soul Sphere is a variation that costs no MP, has a range of 4 and is learned from the Arch Sword for 300 AP. It can be used by Templars. It deals area damage to MP and the element is dependent on the weapon equipped.
Rasp is an Templars and Alchemists ability that depletes the MP of units in a small area. It can be learned for 250 AP from the Apocalypse for Templars and Energy Mace for Alchemists. It costs 8 MP to cast and has a Range of 3.
The original name, "Rasupiru" ("Raspir"), is derived from the name of another related spell, "Asupiru" ("Aspir"). While "Aspir" appears to be derived from either the word "Aspirate" (meaning "to draw in by suction,") or the French version of that word, "aspirer," "Raspir" seems to be simply another level of that spell, being given the prefix "ra-" to denote that (the spell "Rahealra" is another example of the "ra-" prefix being used to denote different spell levels in this vein, and "Basuna" and "Esuna" are a further example of a change in prefix being used to denote different levels of the same family of spells).
Rasp is an English verb whose meaning is to scrape or file down. Since many iterations of the spell throughout the series involve damaging a target's MP or dealing damage over time, this definition is likely the most appropriate.