In case you no longer want to be a connection with someone, you just need to find that specific connection and then click on the ellipsis (⋯) - More Menu - on the right-hand side of the connection row and select Disconnect option.

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You can also perform the bulk deletion by ticking the checkbox on the left-hand side for the connections you wish to delete, clicking on the ellipsis (⋯) in the action bar and selecting Disconnect option.

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Once deleted, you will get the success toast notification.

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Please note that this connection will be deleted from the list of your connections on LinkedIn as well.