No, that is not correct. There is a common misperception that the Mitran priests do not use magic. This is incorrect. This misperception has crept into the rules, however - but that rule is incorrect.
Robert E. Howard, in The Hour of the Dragon, wrote: "When the magic of the Mitran priests failed against the magic of Xaltotun's acolyte…", Clearly Robert E. Howard intended the priests of Mitra to be capable of at least Counterspells and such.
If you go beyond Howard and into pastiche, Dexitheus, who is one of Conan's advisors, is portrayed by L. Sprague de Camp as a spell-casting priest of Mitra. He seemed to do a lot of Divination.
However, the priests of Mitra generally do not appreciate most forms of sorcery, considering it to be the work of demons. For purposes of Conan the Roleplaying Game, the following sorcery styles are considered black magic to the priests of Mitra: Curses; Hypnotism; Nature Magic; Necromancy; Oriental Magic; and Summonings. From The Scrolls of Skelos, the styles of Cosmic Sorcery and Immortality are also considered black magic. As in the case of Orastes, the practice of black magic will get the Mitran priest kicked out of the order.