Sometimes in order to save money, you have to spend money.
A food processor is not a necessity, but it is handy and can save you money in the long term.
Some ways it can save you money:
Making your own almond flour or other nut or bean flours.
Buy the nuts and make your own nut butter- such as peanut butter.
Buy a pumpkin and make your own puree for making pies and breads.
If you have an inexpensive access to apples, make your own applesauce.
You don't have to spend a lot of money on one.
You can find a good one for about $30 or $40, less if you catch one on sale.
If you get one that has a wide enough chute, you can slice whole potatoes or peppers.
They work great to shred zucchini.
I have used mine to make mayonnaise also.
You can use it to mix pie dough or cookie dough.
I mix up my black bean brownies in it.