is it better to refinance your existing home mortgage or pay it off by
selling your investments?

It is almost certainly better to refinance than to sell investments to
pay off your mortgage.
Reasons:
1) The interest you pay on your home mortgage is usually tax deductible.
2) If you sell off investments, you will have to immediately pay taxes
on any gains.
3) The mortgage rate is likely lower than your rate of return on investments.
4) You are probably more diversified if you do not sell of your
investments to pay off the mortgage.

I would have to have more details about your circumstance to give you
a more complete comment, but the above non-specific reasons are enough
to make most people better off not selling investments to pay off
their mortgage.

For peace of mind pay off the mortgage.  
Monday magazine put this questions to a professtor of finance, and he
chose to pay off the mortgage.

If peace of mind is really want you want (very few investors have
peace of mind as their goal), then you should still keep your
investment but make sure it is a very safe investment.  There are CDs
now (completely safe) that earn 6% interest.

Scenario:
Mortgage Rate: 8%
Tax Deduction: 8% * 25% = 2%
Investment Return: 6%

In this scenario with a high mortgage rate and a very low rate of
return, paying off the mortgage saves you 8% - 2% = 6%, and your
investment would have earned you 6%.  It looks like it's a wash,
either way is equal... but consider now that it costs you money to
sell your investment (taxes, possibly transaction costs), and you see
that it is best to keep your investment.

In a more realistic scenario:
Mortgage Rate: 6.5%
Tax Deduction: 1.625%
Investment Returns: 9% (moderate returns, not completely safe but not
extremely risky)

Now you can see that selling the investment costs you a tremendous
amount.  If your mortgage is $200,000 then after 10 years, the cost is
about $100,000.  If you earn 11% (the stock market average for the
last 85 years) then paying off your mortgage costs you $160,000 over
those 10 years.