Twitter is a popular platform to share opinions and claims, which may be accompanied by the underlying rationale. Such information can be invaluable to policy makers, marketers and social scientists, to name a few. However, the effort to mine arguments on Twitter has been limited, mainly because a tweet is typically too short to contain an argument — both a claim and a premise. In this paper, we propose a novel problem formulation to mine arguments from Twitter: We formulate argument mining on Twitter as a text classification task to identify tweets that serve as premises for a hashtag that represents a claim of interest. To demonstrate the efficacy of this formulation, we mine arguments for and against funding Planned Parenthood expressed in tweets. We first present a new dataset of 24,100 tweets containing hashtag #StandWithPP or #DefundPP, manually labeled as SUPPORT WITH REASON, SUPPORT WITHOUT REASON, and NO EXPLICIT SUPPORT. We then train classifiers to determine the types of tweets, achieving the best performance of 71% F1. Our results manifest claim-specific keywords as the most informative features, which in turn reveal prominent arguments for and against funding Planned Parenthood.