No one likes to have that damp basement smell in their house. It’s objectionable and usually means there’s a problem under the foundation with water. Eliminating the problem is a different matter, but there are steps you can take to get rid of the damp basement smell.tep 2 - Cleaning. Clean out the basement and throw away all items that can help contribute to a damp basement smell. This will include newspapers and cardboard. Where there’s damp in the air this can quickly turn to mold and mildew in items like this.