Just some ideas..

[Rio44]

Ok so Im a quantum physicist specializing in quantum enigma, but Ive recently been doing some general knowledge research and was wondering if it was possible to either engineer a virus to infect host cells but caus them to destroy infected cells and then erase themselves or to make the cytoplasm in the cell reject the virus by breaking it down or self destructing?

[AstraSequi]

I'm not sure what you mean by "to infect host cells but cause them to destroy infected cells and then erase themselves."

In general, virus targeting is very specific, so you will not have to worry about infecting both the host and the target you want to destroy, unless the target is hiding within the cells of the host. Engineering from the ground up is not currently possible (we can't really design any proteins), but that's not a limitation since so many viruses can just be taken directly from nature with minor (or no) modifications. If you want a virus to do something that it doesn't usually do, you can build it using components (genes) that are derived from known viruses, but even that is very difficult and I don't think there have been any major successes with it.

You might also find it interesting to look up phage therapy.