Maybe. If you are filing your income tax as a sole proprietor or partner, using the T1 form, when you are filling out Form T2125 (Statement of Business or Professional Activities), you will be listing various business expenses. If your business expenses exceed your business income, you will record a business loss on this form.
Will you get to "use" this business loss and claim the business expenses? That depends on whether or not you have other income. If you do, you may wish to take the income from your business (the non-capital business loss) and use it to offset your other income, in effect, claiming the business expenses.
However, note that non-capital losses can be used to offset other personal income in any given tax year, and can be carried back three years, or carried forward for up to seven years. So you may not want to "claim your business expenses" and use your business loss this particular tax year. It may make more sense for you to carry your non-capital loss back to recover income tax you've already paid, or to carry it forward to offset a potentially larger tax bill in the future.
Although I've used an example of a person filing taxes as a sole proprietor here (using the T1 tax form), the rules for non-capital losses also apply to Canadian corporations.