Why not? They budgeted for it. The remainder of the contract is down to, what, $8M and counting? By August 31, just $4M? If that was the difference in prying a better set of prospects in return, I'd do it. (Conversely, the other team would also likely view $4M as small change, unless as you say they are bumping up right at the tax threshold or something like that.)
A few luxury tax teams will be out. A bunch more frugal/fringe teams will likely be out at that price too (Cleveland, Oakland, Milwaukee, etc.). How many teams have ever taken on $4 mil for a month of a bench bat?
I recall Justin Morneau, who was a bit different hitter than Mauer, but still a professional lefty 1B bat. It took us right up until the August 31 deadline (plus an August HR binge from Morneau?) to convince Pittsburgh to take on the remaining ~$2 mil salary, and all we got in return was fringe 40-man DFA candidates. I have a real hard time envisioning anyone stepping up for $4 mil on Mauer.
Or assuming the Twins were willing to eat it, how many teams have given up a meaningfully "better set of prospects" for a month of a bench bat? That's going to take out those teams too.
Yeah, it's already "budgeted" and we're in a lost season, but I have real hard time imagining the Twins would be particularly eager to eat millions just to get Mauer into a pennant race somewhere else. (Not to mention the PR hit of losing perhaps their most popular player, and in such a lopsided deal.)