No. If you rent out your garage, your whole house does not become a rental property and you do not lose all the deductibility of mortgage interest and property taxes.
The IRS considers that you rent out a portion of your home. That portion has to be determined by you. Any reasonable method to calculate that portion can be used. For example, you could divide the square footage of your garage by the total area of your home, then apply a reduction because the garage in not a livable area.
Suppose that you find that the garage represents 5% of your home. Then you can deduct as rental expenses 5% of your mortgage interest and property taxes. The remaining 95% of mortgage interest and property taxes can be deducted in the Deductions and Credits section under Your Home and be included in Schedule A - Itemized deductions.
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