You can delete projects under your workspace. Hover over a project's thumbnail and select the "Delete Project" option under the settings menu.

Zeplin's Summer Breeze release has a new options button near the project name where you can manage your project, including deleting it. Click on the settings menu near the project's name and select "Delete project…".

Type the project name you want to delete and click on the "Delete" button:

Once a project is deleted, it can not be recovered.