No. The property appraiser assesses all property in the county and is neither a taxing authority nor a tax collector. The property appraiser has nothing to do with the amount of taxes levied or collected.
Three separate government entities each having unique and distinct roles in producing your November tax bill. First, the property appraiser annually appraises all property in your county at the market value as of January 1. Next, each taxing authority within the county sets their own millage rate based on the amount of tax dollars necessary to fund their annual budget. Finally, the tax collector takes the amount of taxes due in order to bill and collect all taxes levied within the county. 

In addition to determining values, the property appraiser accepts applications for and administers property tax exemptions. Several types of exemptions are available.
The type of exemption benefiting the largest number of property owners is the HOMESTEAD EXEMPTION. If you own property which you use as your primary residence as of January 1, you may apply for homestead exemption. This will reduce the taxable value of your home by $25,000, resulting in substantial savings on your property taxes.

Any new exemption or change in exemption status should be filed as soon as possible, but no later than March 1.