If I have an Asic to mine bitcoin and I mine to the point that it no longer becomes profitable to mine them anymore, Can I use the Asic to mine a different cryptocurrency and will the difficulty needed to mine it be higher than if I just bought a new Asic?
An ASIC is an "Application Specific Integrated Circuit". In the case of a Bitcoin miner, the specific application is performing the SHA256 hashing algorithm. That is the only thing the ASIC knows how to do.
So long as the cryptocurrency you want to mine uses SHA256, you should be able to use the ASIC on that currency.