As long as no transactions are against the project/cost center, then you will be able to delete in by carrying out the following process in Dimensions:
Within Dimensions please go to the Costing tab.
Under the Records category select the Projects button.
Select the project you would like to delete and click on the delete button at the top (one of the options on the toolbar).
Alternatively if there are transactions against the project, then you will need to purge (delete) the transactions before deleting, which is why some end users prefer to make the project inactive, just in case it needs to be used in the future. To make a project inactive within Dimensions, the following process will need to be carried out:
Within Dimensions please go to the Costing tab.
Under the Records category select the Projects button.
Click on the Edit button (one of the options on the toolbar).
Click the Project Status to change from Active to a different Status.
Save the Status by clicking on the Save button (one of the options on the toolbar).