Twitter app caches everything you ever touch, it grows without limit, consuming an inordinate amount of storage on the iphone/ipad.
Delete the app, re-install the app, is the only way to clear out Twitter cache files.
If you don't have a huge amount of followers, Tweetcaster is a great alternative. As is the Slices app, it can handle Twitter accounts with thousands of followers. Personally, I prefer Slices but it doesn't have interactions yet.