Can an overseas startup copy a US-patented startup?

While you have not noted that the technology is or involves, for example, software or similar subject matter, it sounds like that is what is patented and covered by a US patent. That being said, note that a US patent prohibits others from making, USING, or selling the patented subject matter within the US. Therefore, if somehow there is "use" within the US, there may be infringement. Consult a patent professional experienced with such types of patents for further information and ramifications.