Shinkansen from Sapporo to Haneda Airport?

Does Shinkansen runs directly from Sapporo Station to Haneda Airport?

or do I have to take the Shinkansen from Sapporo to Tokyo, then transfer from Tokyo Station to Haneda Airport?

Neither Sapporo nor Haneda are connected by the shinkansen.

Currently, the shinkansen goes north only as far as Hakodate. It won't be for another 7-10 years or so until it will be extended to Sapporo. And there are no plans to connect Haneda Airport to the shinkansen network. But it is only a 20 minute train or monorail ride from central Tokyo.

By far the cheapest and fastest way to travel between Sapporo and Haneda is a flight. All your options are explained here:
https://www.japan-guide.com/e/e5306.html

If you tour your way on down, it can be very rewarding - lots of great places to see. But if you want to take a train all the way in one shot, it'll take you close to 9 hours, which is just nuts... and then, take an airplane home after all that? You can fly it on a cheap fare like JAL's Explorer Fare if you're a foreign tourist for about 11,000 yen.

Unless you plan to stop at several cities between Sapporo and Hakodate, such as Hakodate, Aomori, Morioka, or Sendai, or unless you are a super-lover of shinkansen, I wouldn't recommend the itinerary you are thinking of.

Flights between Sapporo (New Chitose Airport) and Tokyo (Haneda or Narita Airport) are numerous and not very expensive. The duration of the flight itself is only 1.5 hours, and even if you include time for boarding, disembarking, and transportation to/from the airports, it will be shorter than 4 hours. On the other hand, traveling that route only by train and shinkansen would take around 8.5 hours or maybe more. That's why I don't think it's a better choice.

I have done Tokyo to Sapporo in a day since the Hakodate extension was put in place (eight hours). I usually break up the trip with stops along the way, but more recently simply flying to save time and expense.
Sapporo to Haneda - four trains (three if you walk from Tokyo Station to the direct line to the airport, but that's a ten minute diversion).