You'll need to disconnect the insert from the liner and pull it out first. Here are instructions from the manual-
Jotul C550 Manual
Removing the Insert for Cleaning
U.S. Direct-connection Only:
1. Disconnect the blower power cord from its
outlet.
2. Open the firebox door and pull the insert out
enough to disengage the surround panel
assemblies by lifting up off of the brackets.
3. Lift up the Left Cast Iron Baffle to disengage the
locator boss from the Front Air Tube, and pull the
air tube forward and out of the side manifolds.
4. Keeping the Rear Air Tube in place, push up on the
Right Baffle and remove the Left Baffle.
5. Lift and remove the Right Baffle.
6. Slide the Rear Air Tube to one side to disengage
it from the Side Manifolds.
7. Remove the retainer pin from the Draw-down
Adaptor. Push up on the draw-down bar to
disengage the adaptor from the insert
8. Pull the firebox and cabinet forward as a unit.
The flue connector, liner, and chimney can now
be inspected and cleaned.
9. See page 12 for reassembly procedures.
You can then use the Sooteater or a regular chimney brush and rods to push up from the bottom. This can get very messy so seal off the fireplace opening as much as you can or attach a plastic garbage bag to the end of the liner with a hole in it for the chimney rod to go through. Wear a breathing mask (cheap at the hardware stores) too.