Theoretical models and numerical simulations have established a framework of galaxy evolution in which galaxies merge and create dual supermassive black holes (with separations of one to ten kiloparsecs), which eventually sink into the centre of the merger remnant, emit gravitational waves and coalesce. The merger also triggers star formation and supermassive black hole growth, and gas outflows regulate the stellar content(1-3). Although this theoretical picture is supported by recent observations of starburst-driven and supermassive black hole-driven outflows(4-6), it remains unclear how these outflows interact with the interstellar medium. Furthermore, the relative contributions of star formation and black hole activity to galactic feedback remain unknown(7-9). Here we report observations of dual outflows in the central region of the prototypical merger NGC 6240. We find a black-hole-driven outflow of [O III] to the northeast and a starburst-driven outflow of Ha to the northwest. The orientations and positions of the outflows allow us to isolate them spatially and study their properties independently. We estimate mass outflow rates of 10 and 75 solar masses per year for the Ha bubble and the [O III] cone, respectively. Their combined mass outflow is comparable to the star formation rate(10), suggesting that negative feedback on star formation is occurring.