I have a request from management to hide the content of a specific sub-site from one of our SharePoint Online Admins. The Admin is not a Global Admin. In other words, is there a way to explicitly exclude an Admin from access to a specific site?
Unfortunately, site collection administrator able to access anything in the site.
The only solution I can think of is to update the site collection administrators configuration within your Central Administration site so that they are populated with users that you do want to be able to access the site (ie: the business users who are the only ones who should have that access). If that is just one person, you can leave the secondary role blank, but you at least need to specify a primary administrator.
For more details check Site collection administrator from accessing a site
The short answer is yes, but it depends on what you mean by an admin. A site collection admin will have access to all the sub sites in that site collection. If you want to restrict them remove their access to the site collection role. A site owner, which as Full Control, will only have complete access to that particular site, all sites that inherit those permissions, and if the admin is added to a SharePoint group that gives them Full Control - they will have access to any site which that group is added to.