A TBM700 pilot reported they descended below the crossing restriction on the approach and received a Low Altitude Alert from Tower.

Narrative

I was in IMC icing conditions with permission to fly the LOC DME approach into ZZZ. I was given a heading which I believed I would stay on until I intercepted the approach. The controller gave me a direct to a fix and I did not believe I had time to input the fix into my autopilot so I kicked it off so I would not fly through the localizer. When I kicked off the autopilot; the plane descended through the altitude of the fix on the approach. At this point I was VMC and had the runway in sight so I chose not to ascend back into IMC and icing conditions. I received a low altitude alert from tower. I informed him that I was VMC and had the field in sight at which time I was cleared for a visual. This is HARD approach and I should have told the controller that I did not have time to input a fix and should have asked to stay on a heading to intercept the localizer. Kicking off the autopilot at that critical stage of flight overloaded my workload and resulted in a descent below the published approach. One should never deviate from a published approach without permission. Even though I got lucky and ended up in VMC conditions; I can't count on this in the future. I should have asked to stay on the heading and let my autopilot share my workload instead of kicking it off. The other problem is ZZZ is so busy that I don't get to fly this approach very often even though it is my home airport. I recently [installed] my avionics and this was the first time I had used them to fly the approach. On a slow day; I am going to go up and practice the situation again with a safety pilot in clear weather.