Deleting and Clearing Your Timeline (Mac & iOS)
How do I delete my timeline?
Open the Accounts screen by tapping and holding on your avatar in the upper left, or by opening the sidebar and selecting the Accounts button. From there, tap and hold on an account to bring up editing mode. Tap on the red "X" next to an account to either delete the account from Twitterrific or to clear the cache, thus clearing the timeline.
Delete the account and re-create it.