I wonder if someone can represent the blockchain encryption problem (used to mine bitcoins) as a TSP-metric problem (where TSP = Traveling-Salesman Problem). Any approach or intuition of the idea to do that is welcome.
No, it is not possible. To think that it would be possible is surely to make a category error. Mining Bitcoin is not an issue of finding the shortest possible route between successful mining events, nor, by the way, is it encryption (strictly speaking).
There is a common feature, of course, between the TSP and Bitcoin mining: the need to save time. But a time solution to a TSP problem is very different from one in Bitcoin mining because the TSP looks to find the shortest route of all, and we have to prove that it is absolutely the shortest. This is nothing like mining Bitcoin.