Hi Erie -
You can, provided that the balance on your mortgage is low enough that you can get a HELOC that exceeds that amount. However, the usual choice would be to refinance the mortgage if you're looking to get a better rate or terms. A refinance will give you a lower rate than you can get on a HELOC, which will be an adjustable-rate loan, so the rate could increase over time as well.
The main advantage of using a HELOC that I can see is that HELOCs are generally interest-only loans during the time you can draw against them, which would offer you some flexibility in making payments for 5-10 years, before you have to begin making payments against loan principle. If that is your goal, you might try to find a lender who'll let you do an interest-only refinance that culminates in a balloon payment after a number of years -- that will likely give you a lower rate than a HELOC.
Some HELOCs are offered with no closing costs, but that may be offset by higher rates and annual fees compared to what you'd pay to refinance. Keep a close eye on the numbers and use a mortgage calculator to compare your options and see what your total costs will be over time.