^ Right, they designated him, possibly for the purpose of sending him to the minors (if I understand that process at all).
Being designated for assignment is basically a less harsh way of telling a player he's been cut. It puts the player on the waiver wire and also lets the rest of the league know that a trade can be worked out for him if he clears waivers. You can
use it to stash a guy in the minors, but you don't do it to guys you really value -- once a player is designated for assignment, you have to trade or release him within 10 days if he isn't returned to the 40-man roster.
With Beliveau, he got hammered in AAA and there are some concerns about his arm. The Cubs also needed space on the 40-man for Jackson, Fujikawa and Villanueva, so at this point Beliveau was pretty clearly considered to be a decent
asset, but expendable. To be stuck in AAA at age 25 isn't a great place for a pitching prospect, in any event.