It's fairly difficult. Sending a player down means exposing him to waivers (meaning another team can claim his contract). Now, that might be good in some circumstances, but in general you don't want to lose a player with no compensation. The highest player contracts also have clauses which can prevent being moved or traded (i.e. the player would have to agree being sent to the minors).

One tool they can use is the Injured Reserve, which allows GMs to backfill a long-term injury with players of equal or lesser value without contributing to the cap. This is what the Leafs' GM Nonis used to free up cap space by trading Clarkson to the Blue Jackets for Nathan Horton, for example. And even then Clarkson had to waive his no-trade clause (which he was classy enough to do).