I looked at the Twins' history of in-season trades when they have been sellers.

The last time the Twins made a trade during the season before the deadline when trying to unload veterans for prospects and got any kind of significant return was 1999 when the Twins traded closer Rick Aguilera and left-hander Scott Downs for pitchers Kyle Lohse and Jason Ryan.
You can read the rest of Minnesota Twins Do Little at Trade Deadline to No One's Surprise at Yahoo! Sports.

Should the Twins have traded Morneau no matter how little was offered? Will August be a better time to make deals?