Final answer:
The statement is false; it was Robert Fulton who significantly advanced steamboat technology with the Clermont, and although Henry Shreve contributed with the steam-powered snag boat, the specifics provided in the question are not confirmed.
Step-by-step explanation:
The statement about Henry Shreve designing a steamboat named the Heliopolis that had a jaw-like device on its bow to pick up and remove snags is false. The historical figure associated with early steamboat technology is Robert Fulton. Fulton is credited with launching the first successful commercial steamboat on the Hudson River in 1807, which was named the Clermont.
This steamboat used paddle wheels and significantly improved transportation on major American rivers, including the Mississippi. Henry Shreve did contribute to steamboat technology, but it was with the invention of the steam-powered snagboat, the Heliopolis, which could clear river snags, albeit without details such as a sawmill on deck being confirmed in relation to his work.