Cancer cells often harbor chromosomes in abnormal numbers and with aberrant structure. The consequences of these chromosomal aberrations are difficult to study in cancer, and therefore several model systems have been developed in recent years. We show that human cells with extra chromosome engineered via microcell-mediated chromosome transfer often gain massive chromosomal rearrangements. The rearrangements arose by chromosome shattering and rejoining as well as by replication-dependent mechanisms. We show that the isolated micronuclei lack functional lamin B1 and become prone to envelope rupture, which leads to DNA damage and aberrant replication. The presence of functional lamin B1 partly correlates with micronuclei size, suggesting that the proper assembly of nuclear envelope might be sensitive to membrane curvature. The chromosomal rearrangements in trisomic cells provide growth advantage compared to cells without rearrangements. Our model system enables to study mechanisms of massive chromosomal rearrangements of any chromosome and their consequences in human cells.