There are external SSD's yes, but to benefit from them you need to use Thunderbolt so that the transfer-method (cable) isn't a bottleneck, there's external TB SSD's, and there's also a SATA-Thunderbolt-adapter. Not sure if USB 3 would be valid, haven't checked yet.
So what you can do is either buy an external SSD, or an internal SSD that you put into a SATA-Thunderbolt adapter, in which case you also need a thunderbolt cable.
The problem with external SSD's is that they're overly expensive per amount of storage, compared to internal ones, also - some of them require external power input. The problem with internal with adapter is compability issues. A problem also with all external boot drives is that there can be slight problems with waking up the computer from sleep etc, since the computer might not power them at all times (if no external power source).