Uninstall the Dropbox application and delete any remnants left behind in order to completely remove Dropbox from your Mac. Removing Dropbox from your Mac does not delete your Dropbox account: You can still access your account and synced files via the Dropbox website.
Delete the Dropbox Application
Click the Dropbox icon on the menu on the top of your Mac's screen to open the drop-down menu, then click the Gear icon and select Quit Dropbox to quit the application. You must quit the application before you can uninstall it.
Open your Applications folder, click and hold the Dropbox icon and drag and drop it onto the Trash icon on the Dock at the bottom of your screen.
Hold down the Control button on your Mac's keyboard, click the Trash icon on the Dock and select Empty Trash to finish uninstalling the Dropbox application.
Delete Your Dropbox Folder
After you delete the Dropbox application from your Mac, you have the option of deleting your Dropbox folder from the computer as well. This folder contains all of the files and other data synced from your Dropbox folder online. Removing this folder is optional. If you decide to delete it, all Dropbox files stored on your computer are removed and can't be recovered unless they've recently been synced with your online Dropbox folder.
Click the Finder icon on the Dock to open a new Finder window.
Click and hold the Dropbox icon under the Favorites heading on the left of the Finder, and drag and drop it onto the Trash icon on the Dock.
Ctrl-click the Trash icon and select Empty Trash to finish deleting your Dropbox folder.
Removal of Remaining Items
Even after uninstalling the application and deleting your Dropbox folder, a few files and pieces of data related to Dropbox remain on your Mac. Remove them to completely clear your computer of anything related to Dropbox.
Open a new Finder window and press Shift-Cmd-G to open the Go To The Folder prompt.
Enter /Library and then click the Go button.
Click and hold the DropboxHelperTools folder and drag and drop it onto the Trash icon on the Dock.
Press Shift-Cmd-G again, enter ~/.dropbox into the prompt and press the Go button.
Select everything in the folder and drag and drop it onto the Trash icon on the Dock.
Ctrl-click the Trash icon and select Empty Trash to finish removing all Dropbox-related data from your Mac.