If the metrics for determining that Jesus was not using hyperbole is that He repeats Himself and that people leave Him, then the topic is still open for debate on whether maiming oneself is only hyperbole or should be taken literally.
Jesus repeatedly said lose one part of your body to save the whole. In Mt 5:29-30, He said pluck out your eye, then He reinforced that and repeated Himself after He said cut off your hand. And later in Mt 18:8-9, Jesus again admonishes the crowd with this command, grouping the foot and the hand together for extra emphasis. Four times Jesus told the people to lose one part of your body to save the whole, compared with five times that He told the people to eat His flesh. The repetition metric has been met.
Regarding people leaving Him when they hear unwanted commands, Mk 9:43-47 presents the same story as Mt 18:8-9. This story in Mark occurs at the end of the chapter. Immediately at the beginning of Mark 10, we read that Jesus then left the place where He was and went to Judea. Since Jesus didn’t stick around, our Gospel author doesn’t know specifically whether people in that place abandoned Jesus because of this or not. However, one could reasonably conclude that people of Jesus’ time were no more interested in becoming blind parapalegics than they were in becoming cannibals (in the manner that they understood it), so the abandonment metric could be met also. And, Jesus doesn’t tell His apostles “only kidding” about this when later they are apart from the crowds.
What about Jesus’ command to the rich young man to sell everything he had, give it to the poor, and come follow Him? This man left Jesus on the spot! (Mt 19:21-22; Mk 10:21-22; Luke 18:22-23). How many among us have followed this command from Jesus? Hyperbole or not? (It meets the abandonment metric.)
So, a cynic would argue that human convenience invokes hyperbole when confronted with a direct command to maim oneself or endure loss, but in the absence of such severe temporal personal injury or loss, taking things literally is fine (and safe!).
The only defense I can find for the hyperbole of the eye-hand-foot thing is, that after the resurrection Jesus did not show up with a knife to cut out Peter’s tongue for having bore false witness against knowing Him three times. But there has to be more than this if we are to be compelling in our conversations with non-Catholics.
Where else is hyperbole used in the Bible, and what supports its recognition as such?