Have the Minnesota Twin's brke ground on their new stadium yet, and if not why am I paying the taxes already?

Answer 1

Construction should begin soon:

Site clearing to begin at ballpark site
Twins, construction company set to break ground on May 21.



The Twins discovered an outdated sewage system beneath the ballpark's construction site. (Twins) No news is good news for Authority
In a last-minute decision, a possible disaster was avoided when an underground sewage system was discovered beneath the site of the Twins' new ballpark. As a result, the Minnesota Ballpark Authority can be sure construction will begin soon.

For more details see: http://minnesota.twins.mlb.com/min/ballpark/index.jsp

As far as your taxes are concerned when building a building there is a lot of cost before ground is even broken so I would assume millions have already been spent on architecture documents, ground surveys, materials purchasing, etc.