Although you can cancel auto and homeowner's insurance claims, the record of the claim and the incident are kept on file. However, a canceled claim will show as a zero payout. When assessing a customer's risk, insurance companies look at the payouts, not just the number of claims. Withdrawing the claim should not have any effect on whether your rates rise or fall.
Contact the Insurance Company
You can cancel a claim by contacting the insurance company and asking for the claims department. If you have the number to your claims adjuster, contact him directly. You'll need to identify yourself and provide your claim number. Tell the adjuster the reason you want to cancel. You can simply state there was a misunderstanding, you can't afford the deductible or you don't want your rates to increase. Depending on the insurance company, you may have to submit a written request or fill out paperwork to confirm you want to cancel.