Matthew 5:27-30 - Did Jesus teach people to literally pluck their eye out and cut their hand off?
In context, Jesus is speaking generally, of any stumbling blocks - not just any one sin, (as suggested in another answer about adultery).
NASB, Matthew 18:7-8 - “Woe to the world because of its stumbling blocks! For it is inevitable that stumbling blocks come; but woe to that man through whom the stumbling block comes! 8 “If your hand or your foot causes you to stumble ...
2. Answer - Can Maiming Oneself Justify Neglecting others who are as Distressed?
At the very least, when Jesus speaks of cutting off your "right hand", he is at the very least speaking metaphorically of one's own strengths and the people they favor the most - if those things are causing stumbling.
"Right Hand" is used metaphorically to indicate strengths and who you favor most:
NASB, Genesis 48:18 - Joseph said to his father, “Not so, my father, for this one is the firstborn. Place your right hand on his head.”
NASB, Psalms 77:10 - Then I said, “It is my grief, That the right hand of the Most High has changed.”
NASB, Psalm 89:13 - You have a strong arm; Your hand is mighty, Your right hand is exalted.
NASB, Matthew 20:21 - And He said to her, “What do you wish?” She *said to Him, “Command that in Your kingdom these two sons of mine may sit one on Your right and one on Your left.”
When interpreted literally, the better question is:
Will maiming yourself actually be as great a stumbling block, and destroy a relationship with God, or stop you from observing the commands of Jesus - like caring for others who are in distress?
That answer would likely deter any from such an extreme form of observance, as the observance would likely cause a greater risk of falling from grace.
This is the reason God commanded people to meditate on his commandment, day and night, (Joshua 1:8). This commandment is way too significant to be invalidated and simply dismissed as metaphor.
Jesus was speaking from divine awareness, knowledge, and experience. So, a modern explanation can reasonably be based on the same principle - experience:
Imagine a father, seeing his newly born daughter for the first time - falling madly in love, only to watch as her life was slowly taken from her, in suffering. Imagine a lifetime of being consumed by that love - knowing that you will never be embraced by it.
Imagine standing before God, in judgement, instantly perceiving the passionate, unrestrained love of God towards you: to know how madly in love God is - for you. And imagine, in that moment - you immediately fall passionately in love with God in return, a consuming love. Then, imagine: "Depart from me you worker of iniquity, (Matthew 25:41)". Then, imagine an age of life never able to express that love, nor ever having that love returned, nor having any hope that your love will be heard.
Anyone that has experienced love in these ways can relate to the consuming desperation that this kind of love and grief brings.
Based on Jesus' own divine awareness and knowledge, he was literally saying - if you only knew the love of God, you would do anything, absolutely anything, to never separate yourself from it.
Ultimately, the controversy of this command is that it leads to a justification to commit suicide, to end the suffering that is causing a person to fall. However, the "solution" - is to also observe the command to bear each other's burdens, (Galatians 6:2) - because people cannot endure alone, even when doing "the right thing".
In other words, the distressed person does not have a justification to neglect others that are distressed - and severing one's own hand would interfere with their obligation to this commandment.
NASB, Matthew 26:38-39 - 37 And He ... began to be grieved and distressed. 38 Then He *said to them, “My soul is deeply grieved, to the point of death; remain here and keep watch with Me.” 39 And He ... fell on His face and prayed, saying [desperately], “My Father, if it is possible, let this cup pass from Me; ...” 40 And He ... *found them sleeping, and *said to Peter, “So, you men could not keep watch with Me for one hour? 41 Keep watching and praying that you may not enter into temptation; the spirit is willing, but the flesh is weak.”