That seems like more evidence of some kind of clumsy political agenda on the board's part, since there's no way actually looking at the budget could give you a picture where Classics and German studies, of all things, are responsible for unsustainable spending increases; they're among the cheapest programs to operate. I suspect it's just some hedge-fund types who don't like the humanities and are looking for excuses to gut them.
If the goal was really to keep costs in line, then the first thing to do would be to assess where the cost increases have come. Which programs have seen the biggest cost increases? And, in which of those are the cost increases worth the quality the program brings to the university? Rank the programs by both expense and quality, and cut the programs which have the highest expense relative to their quality.
Are you basing this on an analysis of UVA's budget? Someone cited somewhere that the Germanic Studies department had like 15 professors. If they faced declining enrollments, they very well could be in a situation where the size of the department isn't justified by the number of students it is teaching.
If the goal was really to keep costs in line, then the first thing to do would be to assess where the cost increases have come. Which programs have seen the biggest cost increases? And, in which of those are the cost increases worth the quality the program brings to the university? Rank the programs by both expense and quality, and cut the programs which have the highest expense relative to their quality.