Most translations in English today have rendered the Greek word airo (αἴρω) in a manner that does not reflect the best understanding of the Greek lexica or of the cultural context of  John 15:2. The translation of the term in John 15:2 is sometimes given as "cut off," or something similar:

NIV: "He cuts off every branch in me that bears no fruit, while every branch that does bear fruit he prunes so that it will be even more fruitful."

NLT: "He cuts off every branch of mine that doesn’t produce fruit, and he prunes the branches that do bear fruit so they will produce even more."

GNT: "He breaks off every branch in me that does not bear fruit, and he prunes every branch that does bear fruit, so that it will be clean and bear more fruit."

Some translations render airo  (αἴρω) in a better way, as "take away," since the phrase "take away" or "remove" is not the same as "cut off" and may allow for the sense of asportation or move from one place to another, but it does not give the whole sense of the word, or the understanding of ancient viticulture.

KJV: "Every branch in me that beareth not fruit he taketh away: and every branch that beareth fruit, he purgeth it, that it may bring forth more fruit."

NKJV: "Every branch in Me that does not bear fruit He takes away; and every branch that bears fruit He prunes, that it may bear more fruit."

WEB: "Every branch in me that doesn't bear fruit, he takes away. Every branch that bears fruit, he prunes, that it may bear more fruit."

ASV: "Every branch in me that beareth not fruit, he taketh it away: and every branch that beareth fruit, he cleanseth it, that it may bear more fruit."

HCSB: "Every branch in Me that does not produce fruit He removes, and He prunes every branch that produces fruit so that it will produce more fruit."

NET: "He takes away every branch that does not bear fruit in me. He prunes every branch that bears fruit so that it will bear more fruit."

ESV: "Every branch in me that does not bear fruit he takes away, and every branch that does bear fruit he prunes, that it may bear more fruit."

The translation "Every branch that doesn't bear fruit, he "cuts off," "chops off," or "breaks off" has no basis whatsoever in Greek lexicography. The definition of every Greek dictionary—of which I have an extensive collection of Greek lexica from the Classical, Hellenistic, Graeco-Roman, New Testament, and Patristic periods of the Greek and Roman world—translates "lift up," as the primary meaning of the word airo, and listed first in the definition of the word. Note proof on this in the following sample list:

aeiro (ἀείρω; αἴρω), "lift up, raise" (Liddell, Scott, Greek-English Lexicon (unabridged, p. 27)

airo (αἴρω), "to move something upwards vertically," "pick up, lift" (Muraoka, A Greek-English Lexicon of the Septuagint, p. 12)

airo (αἴρω), "to lift, to take up," Lust, Eynikel, and Hauspie, Greek-English Lexicon of the Septuagint, p. 16.

airo (αἴρω), "to lift up and carry (away)," Louw and Nida, Greek-English Lexicon of the New Testament, p. 207, sec. 15.203.

airo (αἴρω), "to raise to a higher place or position, lift up, take up, pick up," "to lift up and move from one place to another" A Greek English Lexicon of the New Testament and Other Early Christian Literature, p. 28.

airo (αἴρω), "to raise, take up, lift or draw up," A Manual Lexicon of the New Testament, p. 13.

airo (αἴρω), "to raise, hoist" Sophocles, Roman and Byzantine Lexicon, Vol 1, p. 95.

aeiro, airo (ἀείρω, αἴρω), "to lift up, raise," Lampe, A Patristic Greek Lexicon, p. 38.

In addition, the church father Jerome, in the Vulgate, translates the Greek word (αἴρω) airo in John 15:2 into Latin: "omnem palmitem in me non ferentem fructum tollet eum et omnem qui fert fructum purgabit eum ut fructum plus adferat." The Latin word "tollet," is a third person singular verb from "tollo" meaning "to lift, raise up, or elevate." See Cassell's New Latin Dictionary, p. 606.

Why is the use of "lift up" as the first meaning given for the word airo (αἴρω)? It is because the first meaning should be considered, and given priority, before moving to other possible meanings. What is important in this context is the setting of viticulture, and the practice of growing grapes in ancient Israel (and even modern Israel), is that those who care for vineyards did not cut off branches that were not growing grapes. They lifted them up off the ground to receive more light, and away from moist ground and insects, to give them the help to grow grapes. 

In view of the overwhelming evidence that αἴρω has a primary meaning of "raise, lift up, or take up," why would anyone translate the word as "take away," a secondary meaning, and especially "cut off, or break off" totally absent in all of the lexica of the Greek language? This would be the natural meaning of the word as used by Jesus in John 15 in light of the commonly understood practice of vineyard workers attempting to help branches grow grapes. 

I suspect one of two reasons may be given for this poor translation. One is that it is due to translators who don't really take the time to work through the meanings of Greek words but simply follow what has been given in other translations. So translation after translation simply copies one another. I know of one popular contemporary translation that allotted only a few minutes per verse for its translators, whereas it may sometimes take even hours to study the meaning of words, the grammar, and syntax of some difficult or unfamiliar verses in Greek and Hebrew to provide an accurate translation. This is very unfortunate but is reflected in the accuracy of the translations. The second possible reason is that in John 15:6 the text speaks of branches that are later thrown into the fire that were not part of the vine. This causes many to read the statement in John 15:2 wrongly, that if a believer does not produce fruit, then the vinedresser (God) cuts them off and sends them to hell. So, the bad translation may come from a theological position and then be injected into the text, rather than from the lexical and cultural context.

See the passage study on John 15:1-6 in the HVSB by Dr. Gary Derickson entitled "Jesus' Discussion on Disciples Who Are Not Abiding in Him." Dr. Derickson has a master's degree in horticulture and a doctorate in Bible exposition and wrote an important article on John 15:2-6: "Viticulture and John 15:1-6" (Bibliotheca Sacra 153 (January-March 1996) 34-52). You may also read his discussion on abiding in Christ found on this page of the HVSB.