The present study argues for the pivotal role that the principle of economy - linguistic and cognitive - plays in translating English argumentative texts into Arabic. The study investigates, within the framework of relevance theory, the hypothesis that if some ST information is irrelevant to the TL decoder, it will most probably entail him to further process that information and cause him to be overloaded cognitively. Moreover, based on the realization of cognitive environment shared by the SL communicator and the TL decoder, it is hypothesized that the background knowledge and the cultural aspect are of great importance in giving an adequate shape of an argumentative text in the process of translation.To carry out the analysis, an English argumentative text has been selected in order to examine how the principle of economy affects the process of translating English argumentative texts into Arabic by applying the "Relevance Theory" as a model. The study concludes that there is a balance between economy and redundancy; the latter is indispensable in clarifying vague information and unfamiliar reduced forms of expressions, the former is also necessary to save the reader time and effort in processing the information