Yes you can buy nice clothes here in Placencia, There is a resale store and about 2 popular boutiques that sell American brands such as American Eagle, Hollister, Forever 21 etc.
For the most part people usually drive up to Belize City, which is approximately 3 hours driving, or if you catch a plane, it's 45 minutes. There are many clothing stores there, but not like the huge malls in the States. To get mall experiences people travel to Chetumal, Mexico, which is right on the border of Belize, and where you will find American outlets.
Some people order online and have their purchases shipped through the post office. Expats have an advantage, because when visiting home countries they usually do their big shopping and bring as much summer clothing as possible!
(Denim romper from Forever 21 clothing store, pictured.)