Artificial self-replication and exponential growth holds the promise of gaining a better understanding of fundamental processes in nature but also of evolving new materials and devices with useful properties. A system of DNA origami dimers has been shown to exhibit exponential growth and selection. Here we introduce mutation and growth advantages to study the possibility of Darwinian-like evolution. We seed and grow one dimer species, AB, from A and B monomers that doubles in each cycle. A similar species from C and D monomers can replicate at a controlled growth rate of two or four per cycle but is unseeded. Introducing a small mutation rate so that AB parents infrequently template CD offspring we show experimentally that the CD species can take over the system in approximately six generations in an advantageous environment. This demonstration opens the door to the use of evolution in materials design.