This study extracts the comments from a large scale of Chinese EFL learners' translation corpus to study the taxonomy of translation errors. Two unsupervised machine learning approaches are used to obtain the computational evidences of translation error taxonomy. After manually revision, ten types of English to Chinese (E2C) and eight types Chinese to English (C2E) translation errors are finally confirmed. There probably exists three categories of top-level errors according to the hierarchical clustering results. In addition, three supervised learning methods are applied to automatically recognize the types of errors, among which the highest performance reaches F1 = 0.85 on E2C and F1 = 0.90 on C2E translation. Further comparison to the intuitive or theoretical studies on translation taxonomy shows some phenomenon accompanied by language skill improvement of Chinese learners. Analysis on translation problems based on machine learning provides the objective insight and understanding on the students' translations.