The reason why it’s tricky to disconnect the university area boundary from the ways is because it’s actually defined as a closed polygon in terms of those ways as a “relation”. If you have a look here:
and zoom in and out you can see the relation and the ways that it consists of. Within the iD editor you can see the existence of the relation by clicking one of the constituent ways (roads) and scrolling down to “all relations” at the bottom left. If you click where it says “all relations” and then where it says “University Grounds” you’re now editing the university. You can click “all members” to see the ways that currently make up the relation, remove those that you don’t want to be part of it, and after doing that add any new ways to it by clicking on them and selecting “add to relation” and then the relation to add to, making sure that it stays a closed polygon.
If that sounds a bit combersome, it is; and it’s one of the reasons why why I’m not personally a fan of defining relations in this way (the other is that the university doesn’t really exend to the middle of the road, does it?).
My personal suggestion would be that instead of defining the university in this way you draw a new way (or maybe extend the existing http://www.openstreetmap.org/way/353690145 , which is part of the university but not a road) and either move the university tags to that, or make that the only member of the existing university multipolygon. However, I’d definitely check with other local mappers first including the author of http://www.openstreetmap.org/changeset/31969946 (which describes itself as “Made Seattle U a multipolygon”). There may be some perfectly logical reason for that that I don’t understand.
One more thing - you’re currently using the default iD editor (you get that by default if you just click “edit” and you’re not using Internet Explorer). iD does allow you to get at “relation” functionality within OSM, but it does try not to be too “in your face” about it. Other editors such as JOSM and Potlatch2 present relation information in a different way which you might find easier to work with here. There seems to be a significant minority of users of any editor X that thinks that if only users of editor Y moved to X, there’d be few data problems, more mappers, etc.etc. I suspect that at least some of those people with fixed opinions about “which editor to use” are wrong…