Terms of insurance policies can vary but yes, generally your slashed tires would be covered by your comprehensive coverage.
Most insurance carriers would see this as an act of vandalism, which is covered under comprehensive coverages. You should place a claim with your insurance company for the damages to the tires. You will owe the deductible amount you chose for the comprehensive portion of your policy.
Keep in mind that you normally can not receive betterment due to a claim. The intention of the insurance policy is to return things to the way they were before the loss or damage occurred. Sometimes, when items are repaired or replaced the policyholder will end up with something that is better than it was before the loss. This is defined as betterment.
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To return your vehicle to the way it was before your tires were slashed would technically mean replacing the tires with ones that had the same mileage and wear and tear on them. That would be indemnity for the loss, returning the vehicle to its state before the damage occurred but it is doubtful that many policyholders would want used tires as replacements.
[Let CarInsurance.com help you find affordable auto insurance now.] To not end up better than before this damage was done to your tires, the insurance company will likely take into consideration the mileage as well as the wear and tear of the tires that were slashed and may require you to pay the difference between what they were worth and the price of new tires. You will need to talk to your claims adjuster or agent to see if this will be an issue for you. | 
