There are different options to delete contacts from a campaign depending on the campaign status. 

If the campaign is in progress or scheduled you can delete the contact from the campaign in the contact profile. To do so, you can go to the contact profile and select the campaign option. 

If the campaign is in any other status (failed or completed) you won't have the possibility to remove the contact from the profile but you can do it from the Campaign Dashboard

You can see all the campaign information in the dashboard, you can filter the list by keyword, name, scheduled date, created by or status: 

Once you select the campaign you are looking for you can double-click on its name and a new screen will pop up, here you'll see the campaign information as well as the contacts added to it and their status on the campaign.
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To cancel/delete contacts from a scheduled or in progress campaign you click on the campaign name and will open a new screen with that campaign information, here you can click on the option of add or remove contacts from a campaign:  
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To remove the contacts from the campaign you have to click on the "x" next to the name and then click on Save

There you have it, now if you want to remove a contact from a campaign you'll be able to do so by following these steps. 😎