It is thought that, and the heart is the problem, but if we cannot resist the temptation of some thing that entices us to sin, esp. if it is needed or actually useful, like booze, then it should go out. And we should be sensitive to what grieves the Spirit of Christ, though I often do, even if to a degree. Obviously there are things that can be used for good or evil, like the Internet instance, and thus cutting such off is a prayerful decision. Sex addicts should if porn cannot be avoided.
That admonition appears to use hyperbole to convey the seriousness of sin...not to encourage people to pluck out their eyeballs.