Matthew 18:8-9
8 Wherefore if thy hand or thy foot offend thee, cut them off, and cast them from thee: it is better for thee to enter into life halt or maimed, rather than having two hands or two feet to be cast into everlasting fire.
9 And if thine eye offend thee, pluck it out, and cast it from thee: it is better for thee to enter into life with one eye, rather than having two eyes to be cast into hell fire.
Mark 9:43-48
43 And if thy hand offend thee, cut it off: it is better for thee to enter into life maimed, than having two hands to go into hell, into the fire that never shall be quenched:
44 Where their worm dieth not, and the fire is not quenched.
45 And if thy foot offend thee, cut it off: it is better for thee to enter halt into life, than having two feet to be cast into hell, into the fire that never shall be quenched:
46 Where their worm dieth not, and the fire is not quenched.
47 And if thine eye offend thee, pluck it out: it is better for thee to enter into the kingdom of God with one eye, than having two eyes to be cast into hell fire:
48 Where their worm dieth not, and the fire is not quenched.
The above passages are sometimes used to teach a vague form of works Salvation, the line taken being something to the effect of "since Jesus said you have to be willing to cut your hand off to avoid Hell, obviously it requires extreme personal effort to not be sent to Hell".
With this in mind, let's analyze these parallel passages.
Neither of these passages are aimed at a believer. Rather, both follow the condemnation of someone who would seek to persuade a child believer to abandon their faith in Christ to join them in unbelief:
Matthew 18:6
6 But whoso shall offend one of these little ones which believe in me, it were better for him that a millstone were hanged about his neck, and that he were drowned in the depth of the sea.
Mark 9:42
42 And whosoever shall offend one of these little ones that believe in me, it is better for him that a millstone were hanged about his neck, and he were cast into the sea.
Therefore, Christ is imploring someone to, basically, remove absolutely anything in their life that would prevent them from "entering into life", which as we know from elsewhere in Scripture, is achieved by putting their faith in Him (John 6:47: 1 John 5:12).
This is similar to something Christ said in Matthew 5:29-30, which is covered in another article. In that passage, I believe Christ is emphasizing the extreme requirements of the Law as the standard of righteousness, whereas here He is more emphasizing His own importance, and how grievous an offense it is to not believe in Him. In both cases, Christ is using hyperbole, to demonstrate the extreme importance of what is being discussed.
Even if someone lacked a hand, or foot, or an eye, without putting their faith in Jesus, they would still come into condemnation (John 3:18). In these passages, Christ is teaching that whatever obstacles there are to faith need to be removed with malice, regardless of the cost, given what's at stake.