I'm on my phone, but I follow the TWolves rather intensely (although not as intensely as the Celtics, of course

). This is by no means a tanking move.
Budinger was almost an almost universal disappointment last year. He was billed as a floor-spacer, but he shot a very mediocre percentage from deep. He also seemed to have lost athleticism, dunking less than once every two games (after dunking about once per game before a knee injury). This post-surgery struggle led many to question his long-term organizational role. Picture Jason Terry when he signed with the Celtics- an expected above-average role player that disappointed.
Last year, the Wolves were decimated by injuries. Muhammed, Pekovic, Rubio, and K-Mart all missed more than half of the season, and I believe Dieng missed all of April and May. Not to mention trading Glenn Robinson III, Mo Williams, Corey Brewer, and Thad Young mid-season. Budinger played the 4th most games and 6th most minutes because the TWolves often had nine or less available players, and many of them were shipped out as the year went by.
Another factor to consider is that the Wolves view Lavine as a SG. With Rubio healthy and Tyus Jones in the fold, that pushes Lavine to second-string two guard (behind Kevin Martin). This pushes Wiggins to his assumed natural SF spot and makes Muhammad the back up. On top of that, the Wolves just signed reigning Euroleague MVP Bjelica, who plays SF/PF. With Towns and Garnett at PF and Pek and Dieng at center, Budinger was, at best, a third-stringer at two positions. That doesn't even mention Payne and Bennett.
Also, the Wolves most likely won't deal Rubio. His on/off differential was astounding, as the Wolves were above .500 with him playing. He also provides positional balance.