save money up (for something)
To put aside money in small increments in order to accumulate savings, as for some particular purpose or future use. A possessive pronoun can be used between "save" and "money." We'll have to save our money up if we want to take that vacation to Greece next summer. I've stopped eating out at restaurants so I can save some money up for a new car.
save money up (for something)
to accumulate an amount of money for the purchase of something. I'm saving my money up for a car. Save up your money for a car.