I already used DotSpatial in a few projects. It is fine for reading/writing shapefiles, clipping etc..
According to the DotSpatial documentation, it is possible, to create WebGis projects, but I wonder why I cannot find any on the Web? Also, I wasn't able to find any tutorial for it. On GitHub there is a sample project called DemoWeb (https://github.com/DotSpatial/DotSpatial/tree/master/Source/Examples/DemoWEB) but I wasn't able to get it running.