Maciek Czarnik answer does not worked for me, but it got me insights what to do.
iOS 7+
Swift
textView.textContainer.maximumNumberOfLines = 10
textView.textContainer.lineBreakMode = .byTruncatingTail
ObjC
textView.textContainer.maximumNumberOfLines = 10;
textView.textContainer.lineBreakMode = NSLineBreakByTruncatingTail;