The Earth's mantle is chemically heterogeneous and includes primordial material inherited from early planetary processes, which probably led to an initial depth-dependent composition of radioactive elements. One consequence is that its internal heat sources are not distributed homogeneously. Mantle convection induces mixing, such that the flow pattern, the distribution of heterogeneities and the thermal structure are continuously evolving. We studied these phenomena in the laboratory using a unique microwave-based experimental set-up for convection in internally-heated systems. We characterize the development of convection and the progression of mixing in an initially stratified fluid made of two layers with different physical properties and heat production rates. In analogy to the Earth's mantle, the upper layer is thicker and depleted in heat sources compared to the lower one. Two different convection regimes are identified, a dome regime and a stratified regime. In the dome regime, large domes of lower fluid protrude into the upper layer and remain stable for long time-intervals due to their enhanced heat production. In the stratified regime, cusp-like upwellings develop in association with deformation of the interface separating the two fluids. Upwellings are similar in size and morphology to those that would be generated by heating through the tank base, implying that mantle plumes are not necessarily due to heating by the Earth's core. These plumes are made of heated upper layer fluid and enriched lower fluid in variable proportions giving rise to a range of plume compositions. Mixing proceeds by two mechanisms: shearing of thin slivers by viscous coupling at the interface between the two fluids, and trapping of upper fluid within the lower fluid through folding. Empirical scaling law for the mixing rate allows extrapolation to planetary mantles.