You won't lose anything by saving part of your monthly income.
Literal
Every-month [possessive-の] income [possessive-の] a-part [object-を] save [conditional-すれば] loss [topic-は] not-exist.
~すれば損はない ('if you do X, there's no loss') is a practical way of recommending something without strong obligation. 収入の一部 ('a portion of income') chains two の-linked nouns. 貯蓄する is a formal verb for saving money.