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Open the LinkedIn app. Tap the search bar. Type in a person's name. Tap their name. Tap the "..." button. Tap Remove Connection. Tap Remove connection when prompted.
If you're logged into LinkedIn, doing so will open your profile's Home page. If you aren't logged in, tap Sign In, enter your email address and password, and tap Sign In. It's at the top of the page. Alternatively, you can tap My Network at the bottom of the screen. This should be the name of the person with whom you want to remove a connection. If you're using the My Network tab, tap [number] Connections in the top left corner. It should pop up below the search bar. If you're in the Connections menu, scroll to your person's name and tap it. It's in the top right corner of the screen. It's about halfway down the drop-down menu. It's at the bottom of the screen. Doing so will remove the person from your connections. You can also tap Following in this menu and then tap Unfollow to stop viewing updates from their profile.