Can I use my tenants security deposit to cover insurance deductible?

NO! They are not responsible for the deductable. They are responsible for the acutal cost of the damages but you cannot make them pay any portion of your insurance cost. 

Even if they were you CANNOT use the deposit for that.  The deposit is not to be used for anything until they move out. 

Sure--it will be part of the damages you can assess to the tenants. 

You need to send the bill for the deductible to the tenants and they need to pay it themselves.  The security deposit cannot be touched until they move out and if there is damage done. 

WHERE?  In MY State the security deposit MUST be held in a separate account until the term of the rental ends.  You CANNOT use the security deposit to make repairs, pay a deductible, anything else.  The tenant moves out AND the landlord returns the security deposit plus interest minus any damages.

I own and manage 3 rentals.

That depends on the landlord-tenant law in your state. Some states require deposit to be escrowed and it cannot be touched until you go through the required process for keeping deposit AT THE END OF THE TENANCY.  Not all states do that, but in most, you still cannot take the deposit until you document damages at the time the tenant vacates.  In most states, you would have to file a lawsuit to recover this kind of tenant-caused damage, and you would have to cover the deductible out of your own pocket.

That is not what the deposit is for, it is for after they leave and damage done once you inspect. I have to assume you live in a country where the deposit is not insured in a scheme and landlords are allowed to hold it themselves in which case you need to read the stauatory laws regarding this...regardless of that as you say the tenant is resonsible... you need an invoice for the work and present it to the tenant to pay...or you have landlord insurance which may or may not cover this, but speak to your insurer if covered they will pay and contact the tenants insurers or the tenants to pay the bill

It is indeed their responsibility.  See if they have a renter's policy first.

Yes but you should first bill them.  Demand payment within 10 days.  If they don't pay, then take it out of their deposit and request that they replenish their deposit.  You should also ask them for their renter's insurance info.  If they had it, give that info to your insurance company, who is entitled to recover what they paid out, and who will likely be checking into that anyway.