The portion of the credit card purchases that you receive back in cash does not constitute gross income (i.e., not taxable).
See https://www.irs.gov/pub/irs-wd/1027015.pdf
However, if the purchase was a business expense, you cannot deduct the portion you receive in cash back from your business income (e.g., You purchase $500 in office supplies and receive $25 cash back. You can deduct $475 ($500 less the $25 "discount").
See https://turbotax.intuit.com/tax-tips/irs-tax-return/video-are-cash-back-rewards-taxable-income/L1FWH...
