His parents owned a hardware store. As with many future artists, he displayed an early affinity for drawing. His first formal studies were in 1849 with Domènec Soberano, a local wine merchant and amateur painter. In 1853, he and his fellow student, Marià Fortuny, were given the opportunity to exhibit at a showing held by the Casino de Reus.
Later that year, he and Fortuny enrolled at the Escola de la Llotja, where he studied with Claudi Lorenzale, a painter associated with the German Nazarene movement, among others. At this time, he produced mostly historical and religious scenes. In 1857 he, Fortuny and two others were given the opportunity to compete for a grant to study in Rome. Fortuny was chosen and Tapiró moved to Madrid, where he enrolled at the "Escuela Superior de Pintura y Grabado", a branch of the Real Academia de Bellas Artes de San Fernando. His instructor there was Federico de Madrazo. He returned to Barcelona in 1860 and assisted with decorating the façade at the Palau de la Generalitat de Catalunya.