"She cuts the apple."
Translation:Lei taglia la mela.
No, the gender of the apple is always feminine. We don't know whether a male or female (or transgender, for that matter!) is cutting the apple. If you were in the conversation you'd probably know by inference or context.
If you want to be explicit -- HE cuts the apple = LUI taglia la mela. SHE cuts the apple = LEI taglia la mela. I cut the apple = IO TAGLIO la mela. YOU cut the apple = TU TAGLI la mela.
Refer to the rest of the conjugation table here: http://www.duolingo.com/word/it/tagliare/Verb :)
The end of verb shows who commits the act so you can omit the pronoun and use only "taglia".
The pronoun can be specified for clarity. For example, if you were talking with your friend about different people and the verb can be applied to each of them. So you have options: lui taglia - he cuts; lei taglia - she cuts.
In addition: Lei (with a capital letter) taglia - you (singular and formal) cut.