Young star clusters are dynamically active stellar systems and are a common birthplace for massive stars. Low-mass star clusters (∼300−103 M⊙) are more numerous than massive systems and are characterized by a two-body relaxation time scale of a few Myr: the most massive stars sink to the cluster core and dynamically interact with each other even before they give birth to compact objects. Here, we explore the properties of black holes (BHs) and binary black holes (BBHs) formed in low-mass young star clusters, by means of a suite of 105 direct N-body simulations with a high original binary fraction (100 % for stars with mass >5 M⊙). Most BHs are ejected in the first ∼20 Myr by dynamical interactions. Dynamical exchanges are the main formation channel of BBHs, accounting for ∼40−80 % of all the systems. Most BBH mergers in low-mass young star clusters involve primary BHs with mass <40 M⊙ and low mass ratios are extremely more common than in the field. Comparing our data with those of more massive star clusters (103−3×104 M⊙), we find a strong dependence of the percentage of exchanged BBHs on the mass of the host star cluster. In contrast, our results show just a mild correlation between the mass of the host star cluster and the efficiency of BBH mergers.