Don't delete users! You can, but don't. Skip to the last paragraph if you decide to forego this advice. You've been warned!
There's a better way to make a user no longer appear in any of the drop-down selectors without deleting the user and finding later that you need to pull out historical data regarding that user in a report.
The best practice for de-activating users who are no longer with the company is to remove all of the system-role checkboxes. Most importantly, Active and Project Resource.
Project Resource allows the resource to show up in the interface even though the resource cannot use Project Insight if they're inactive. An inactive resource who is also a Project Resource can be used for other purposes such as placeholders, or resources who might be made active later as needed. A user who is no longer a Project Resource will still show in the results on reports, but will not be available in the report filters. If you do need to use a resource filter on a person who is no longer a Project Resource, you will need to temporarily make them a Project Resource.
Have you decided to delete the user anyway? Save the user profile as inactive first. Next, click the hyperlink (not the edit icon) for the user by clicking on the first or last name. In the detailed view of the user's profile you will see the delete icon in the upper-right allowing you to delete the inactive user. It will warn you one more time, just in case we haven't warned you enough in this article.