I have a home office. Can I deduct expenses like mortgage, utilities, etc., but not deduct depreciation so that when I sell this house the basis won't be affected?

Regular Method - No, all allowed or allowable depreciation must be considered at the time of sale. You can generally figure depreciation on the business use portion of your home up to the gross income limitation, over a 39 year recovery period and using the mid-month convention. As long as you determine actual expenses and the correct amount of allowed or allowable depreciation, the depreciation reduces the basis of your home accordingly, whether or not you actually claim it on your tax return.  

Simplified Option - There's a simpler option, as announced in Revenue Procedure 2013-13, where qualifying taxpayers may use a prescribed rate ($5 per square foot limited to 300 square feet) to compute their business use of home deduction. This option used in lieu of determining actual expenses has the advantage of reducing taxpayers' recordkeeping burden. Under this option, depreciation is treated as zero and won't reduce the basis of your home. For more information, visit Home Office Deduction, Simplified Option for Home Office Deduction, and FAQs – Simplified Method for Home Office Deduction. In addition, under this optional method, taxpayers can still deduct business expenses unrelated to qualified business use of the home for that taxable year, such as advertising, wages, and supplies.