State-of-the-art weakly supervised text classification methods, while significantly reduced the required human supervision, still requires the supervision to cover all the classes of interest. This is never easy to meet in practice when human explore new, large corpora without complete pictures. In this paper, we work on a novel yet important problem of weakly supervised open-world text classification, where supervision is only needed for a few examples from a few known classes and the machine should handle both known and unknown classes in test time. General open-world classification has been studied mostly using image classification; however, existing methods typically assume the availability of sufficient known-class supervision and strong unknown-class prior knowledge (e.g., the number and/or data distribution). We propose a novel framework WOT-Class that lifts those strong assumptions. Specifically, it follows an iterative process of (a) clustering text to new classes, (b) mining and ranking indicative words for each class, and (c) merging redundant classes by using the overlapped indicative words as a bridge. Extensive experiments on 7 popular text classification datasets demonstrate that WOT-Class outperforms strong baselines consistently with a large margin, attaining 23.33% greater average absolute macro-F1 over existing approaches across all datasets. Such competent accuracy illuminates the practical potential of further reducing human effort for text classification.