The blinkfeed page is a feature of the default launcher which means using an alternative launcher (I like Nova Launcher) will replace it.
As for whether you can keep the default launcher but disable Blinkfeed, that may be more difficult. I've seen a tutorial for how to do it on the One X, saying there is an option under “Settings” > “Personalize” > “Customize home screen” for replacing the "Blinkfeed" home screen with a "classic" home screen. But I haven't found that in the One Mini.