Using widget logic requires a little finagling to get what you want. It uses WordPress conditional statements.
To remove widgets from a particular page, you must use the corresponding conditional. In this case the blog page is usually accompanied by the conditional statement of "is_home()". Therefore, to remove widgets from this page you must use a reverse conditional "!is_home()". The "!", in a sense, means that you actually mean the inverse of the statement, which all in all menas, "I want this widget to show up anywhere, except the where "is_home()" is "true" (the blog page).
I know this can be somewhat complicated, let me know if I should try to be any clearer. I actually have my own widget plugin that may help, but without seeming like a shameless plug, I won't post a link unless you ask me ;)