Can we force a species to evolve through a mixture of natural and artificial selection in a closed environment?
Selection (whether natural or artificial) is one of the force causing evolution. So yes, artificial selection is one way to 'force' evolution to happen in a specific way. One could select trees for bigger fruits or dogs for longer fur for example. One cannot force "Natural Selection", as "forced natural selection" is defined as "artificial selection".
You might want to have a look at an intro to evolutionary biology such as Understanding Evolution by UC Berkeley for example
Yes, we can. One example is pushing bacteria to evolve antibiotic resistance by putting them under artificial selective pressure, i.e. adding antibiotics in the medium. You can find it here http://gizmodo.com/watch-as-bacteria-evolve-antibiotic-resistance-in-a-gig-1786389688
In addition to what others have replied, perhaps what you're referring to is speciation, i.e. can you force a species to evolve into a new one that is a distinct species from the original one? I'd say yes, but if you wanted to be quick about it then you'd have to choose an organism with a very short generation time, subject them to different selective pressures than the original population are subjected to and prevent the two populations from mixing and interbreeding. I guess you could say a new species had evolved when they can no longer produce viable offspring with the original population. Might take a while though. In fact maybe this would work better/be quicker with an asexual organism but it would be more difficult to identify the point at which a new species had evolved.