I am currently reading A Song of Ice and Fire (just finished CoK) and I am really scared that I will accidentally read a question title that will spoil something really big for me. Is there a way to exclude a particular tag from your search results?
Yes: use a minus sign.
[a-song-of-ice-and-fire] gives you all questions with that tag; searching for
[a-song-of-ice-and-fire] -[a-storm-of-swords] will give you all questions tagged with the first tag but not the second.
However, be warned: not all questions that concern material from A Storm of Swords will be tagged as such! If you want to avoid spoilers altogether, you'll be better off setting the entire a-song-of-ice-and-fire tag (and game-of-thrones for good measure) on ignore.
And if you see anything about the Red Wedding or the Purple Wedding, read no further!