There are a host of reasons why the evolution of life on a planet like this will be very, very unlikely.
Planetary Magnetic Fields are produced by hot spinning metals, such fields then help to protect said world from cosmic rays, solar winds and other forms of extra terrestrial radiation such as that emitted by stars. Without a conducting fluid core, may that be iron or other such material, the planet will have no means of projecting a sufficient magnetic series around itself, hence leaving its surface venerable to the harsh conditions of space; this surface will be bombarded by fast moving off-world particles primarily in the form of solar winds, ceasing to have a functional atmosphere, leading to climate cooling (lack of greenhouse effect) and the eventual loss of liquid water on the planet leading to the inability for life as we know it to even exist let alone evolve.
Metals are also dense, adding to the planets overall mass and its structural integrity, removing all said metals off world will lead to a dramatic reduction in planetary mass and therefor reduce the bodies surface gravity- further jeopardising any functioning atmosphere present as well as result in a decreased core temperature (pressure at the planets centre of mass dependant on the amount/mass of material surrounding it). Yes, the decay of nuclear materials plays a part in the constancy of heat at the core/inner mantle, but this energy release alone will not be enough to maintain a fluid planet centre. Saying this though, radioactive material decays continually - by expelling neutrons, electrons or protons - in a bid to produce a stable nucleus (the rate it does this is defined as its half life. If protons are radiated from an atom to gain stability, it forms a new element (such as lead from uranium). This makes it possible therefor for radioactive elements to transmute into various transition metals.
Through the decay of radioactive sources, over the course of many millions of years in the correct conditions, reserves of metals can be increased, yet this will not aid in creating a sustained atmosphere or re-establishing the planets mass, in fact, with such nuclear substances now stable, there will be a further decrease in core temperature that will eventuate, in conjunction with the other listed factors in a dead planet with no way of sustaining life as we know it.
Elements such as iron and copper are vital for life, an organisms cells using these metals to produce red blood cells that carry oxygen around the body. Without enough blood cells, the body cannot effectively carry/provide oxygen around it's systems, resulting in many terminal problems the most serious being death. As mentioned by others, calcium (Ca), phosphorous (P), magnesium (Mg), potassium (K) and all other period 1 and 2 elements are classed as also metals and equally important in maintaining basic biologic functions (the creation of teeth/enamel for instance as well as regulation of nerve/muscle function - and protein synthesis).
From these reasons, it is easy to see how amazing transition metals are in planetary stability and to organic life generally. Without sufficient access to such elements/trace particles the evolution of carbon lifeforms will therefor be almost impossible, stress on almost, for if star trek has taught me anything, its that the universe is a mysterious place where nearly anything can happen given the correct circumstances.
EDIT: here is an Encyclopedia Britannica entry detailing the role of the transition metals in biology. The most important ones are iron, copper, cobalt and molybdenum.