How do I manage / delete my Azure logic app connections

Reference MSDN blog
https://blogs.msdn.microsoft.com/logicapps/2016/04/13/browsing-api-connections-in-the-azure-portal/

Using Powershell to manage connections https://blogs.msdn.microsoft.com/logicapps/2016/03/18/using-powershell-to-manage-api-connections/

There is a first class UI support also available now in Azure Portal

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Update: connections are now supported in the resource explorer

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Let me know if this helps.

For sake of completeness, you can access the API connections associated to your Logic App from the options menu:

API Connections

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