El español no tiene "Phrasal verbs". Para cada caso que en inglés existe un verbo+preposición en español tenemos un verbo. Aquí el cut-off significa cortar. Si tomamos por ejemplo el verbo to "put" y añadimos "off", como verás puede tener en español muchos significados diferentes. http://www.wordreference.com/es/translation.asp?tranword=put%20off

"Off" is a preposition. Prepositions, in different languages, sometimes coincide: She is going TO Paris = Ella va A París. Sometimes they do not coincide: I am waiting FOR Joe = Estoy esperando A Joe. Sometimes there is a preposition in a language, not in the other. She looks FOR the key = Ella busca la llave. He serves God = Él sirve A Dios. In other words... the best way you can learn the use of prepositions in Spanish (or any language) is by learning how they are connected to the verbs, since prepositions are always linked to a verb. Trying to unite the use of prepositions in English to their use in Spanish will not always be beneficial, sometimes, it could be frustrating. There are lots of books focused on the use of prepositions, I would advice you to read some of them, but do it after you have a vocabulary of about 1500 or 2000 words. If you try to do it before, you will not be able to recognise the majority of words used in those books and you will have to spend more time in learning the vocabulary than concentrating in the use of the prepositions.

simplemente se puede usar la palabra " cortar " "acortar " o " podar " Yo corté la rama del árbol

Usaríamos verbos más específicos. Para una sleeve: Recortar Para ramas de un árbol: Podar. Ambos verbos ya implican que cortas y retiras lo cortado.