It depends on what kind of cutter you own. While there are a more than a few companies selling quality cigar cutters, the most popular brands are Colibri and Xikar. Should you want to prolong the life of your cutter, both companies fortunately offer sharpening services.
While it's possible to sharpen part of the blade yourself, the casing prevents sharpening at the edges. To properly sharpen the entire blade, the casing must be removed. The manufacturer has the proper tools. Unfortunately, this can take anywhere from eight to 12 weeks.
If you own a Colibri, take it to the tobacconist where you bought it and ask them to forward it to the manufacturer for sharpening or contact the company yourself directly. If you own a Xikar, the cutter is covered under the company's warranty, and they will sharpen or replace the blades based on their discretion. Visit this page on their website to find out how.
If your cutter uses stainless-steel blades, soak it in a cup of hot water until all the bits of tobacco are free and the gum is soaked off. This should take about an hour. Remove the cutter and dry it thoroughly with a towel. You can also use a blow dryer. The cutting action will be greatly improved.
If you have a dull, plastic, single-blade guillotine, throw it away and buy another one. There's no use ruining a premium cigar trying to avoid buying another $2 cutter.