A cutlass, as in a sword? I don't think swords make very good axes. :) I've tried to chop through trees with a very tough machete with poor results (http://www.amazon.com/Condor-14-Inch-Machete-Leather-Sheath/dp/B004WMFNRW).
Standard practice around here (Florida, USA) is to cut the tree down with a chain saw then use a stump grinder to mulch up the bottom trunk and root ball. This is what was done to several trees in my own yard (over 20 trees in yard).