I think your statement was perfectly understandable, and although it might need very slight adjustment to be beyond criticism, I believe any English speaker would almost certainly understand what you meant. I would guess that the cashier was inexperienced and maybe had not come across this kind of request before.
The only adjustment I would make is to qualify what you are referring to by "some". If you had bought multiple items and wanted to split your spending by paying for some of the items by different means, effectively getting two different bills, you could say:
Can I pay for some of my items in cash and the rest by credit card?
Or, if you'd already divided the items, you could be specific and say:
Can I pay for these items in cash and the rest by credit card?
If you simply meant for the cashier to split the bill by two payment methods without dividing your items across two different bills, you should perhaps make it clear that by "some" you are referring to some of the bill and not some of the items:
Can I pay for some of the bill in cash and the rest by credit card?
Can I pay for part of this in cash and the rest by credit card?