Teachers' growth mindset supportive language (GMSL)--rhetoric emphasizing that one's skills can be improved over time--has been shown to significantly reduce disparities in academic achievement and enhance students' learning outcomes. Although teachers espouse growth mindset principles, most find it difficult to adopt GMSL in their practice due the lack of effective coaching in this area. We explore whether large language models (LLMs) can provide automated, personalized coaching to support teachers' use of GMSL. We establish an effective coaching tool to reframe unsupportive utterances to GMSL by developing (i) a parallel dataset containing GMSL-trained teacher reframings of unsupportive statements with an accompanying annotation guide, (ii) a GMSL prompt framework to revise teachers' unsupportive language, and (iii) an evaluation framework grounded in psychological theory for evaluating GMSL with the help of students and teachers. We conduct a large-scale evaluation involving 174 teachers and 1,006 students, finding that both teachers and students perceive GMSL-trained teacher and model reframings as more effective in fostering a growth mindset and promoting challenge-seeking behavior, among other benefits. We also find that model-generated reframings outperform those from the GMSL-trained teachers. These results show promise for harnessing LLMs to provide automated GMSL feedback for teachers and, more broadly, LLMs' potentiality for supporting students' learning in the classroom. Our findings also demonstrate the benefit of large-scale human evaluations when applying LLMs in educational domains.