I use DocuSign in my company. How could I automatically save signed documents to somewhere all the managers can view?

There are several integrations between DocuSign and 3rd party document management systems and cloud storage such as SharePoint, OneDrive, Google Drive, Box, DropBox, and more. You could implement one of those solutions so that all completed documents automatically get stored in your official repository. You can search the DocuSign website for your preferred tool to determine how to get started with the desired integration.

You could also develop a custom solution. DocuSign Connect service pushes notifications when envelope events occur (such as Completed) so you could create a web listener that receives those notifcations and processes them accordingly to different down stream workflows.