in the folder for the repository template you are using you'll see a number of template files (html and xml files). Find the appropriate template file, edit it with notepad or any text editor and remove the date token.
I would suggest the following method..
1. If it doesn't exist, create a folder in your portal tree named "RepositoryTemplates". ex: /Portals/0/RepositoryTemplates
2. copy the folder of the template you are using from the DesktopModules tree to the Portals tree. For example. If you are using the default template, copy /DesktopModules/Repository/Templates/default to /Portals/0/RepositoryTemplates
3. Now you have a /Portals/0/RepositoryTemplates/default folder. You can now make changes to those files and not worry about your changes being overwritten if you ever have to re-install the module, or install a newer releases of the module.
Now, going back to your original question...
if, for example, you are using the default template, and have a dashboard running in "Latest Uploads" mode. Then the file you want to edit would be.. /Portals/0/RepositoryTemplates/default/dashboard.latest.html
edit it and you'll see that it looks like this..
Just remove the second td tag and change the width of the first td tag to 100% like this..
Save it .. and the date is no longer displayed.