How is Huxley satirizing mysticism in Brave New World?

I would say Huxley is satirizing not mysticism per se so much as forms of worship. His dystopian world has seemingly deified Henry Ford as a symbol of the mechanization that has permeated every aspect of society. The silly sloganeering, as in "Ford's in his flivver, all's right with the world" (a paraphrase of Robert Browning's "God's in His Heaven, all's right with the world") and other expressions, are an outward sign of this new type of worship. Also, the names of the characters—Benito, Mustapha, Hoover, and so on—are taken from political figures of Huxley's own time. Like most dystopian novels, Brave New World is a projection into the future of the societal tendencies of the present. In this case it's a materialistic world where the older values are being discarded and everything is under the state's "managerial" control, including people's DNA through eugenics (selective breeding) and their happiness through drugs. It's the worship of not only a figure like Ford, but of these new "ideals" of civilization as well, that Huxley is satirizing. This is the new form of mysticism in his futuristic scenario.

Mysticism is the experience of direct communion with ultimate reality, spiritual truth, or God (Merriam Webster).
Huxley satirizes not so much the concept of mysticism as the way it is debased in the World State. In place of a mystical union or merger with the godhead, such as one might find in Roman Catholicism, people participate in group orgies that end up with physical mergers—in other words, sex—with other people.
This is part of what John the Savage objects to so strongly in the new world into which he has been thrust. Pursuit of God, of glory, of sacrifice, of something higher than oneself, even if it causes one to suffer, has been replaced with worship of the body and sexual pleasure. Huxley, while making us laugh at the silliness of the "orgy-porgy" ritual, also wants us to question how satisfying it is to the human soul to replace the quest for God or spiritual truth with the quest for sex.