From the main menu, click on 'Publisher'. Then click into the folder for either 'Drafts' or 'Scheduled'. Once a post is selected, press the 'X' or the back arrow (on your device) to exit the post. The mobile app will then display options at the bottom, select 'Remove Post' to delete the post.
Tip: If the scheduled post has a 'Megaphone' icon, this indicates the post is scheduled as part of a campaign the user has enrolled in. A user would need to opt out of the campaign in order to remove the scheduled post.