Your workspace seems to have a lot of unnecessary transformers.
You've explicitly set the Coordinate system of both the ECW and Shp file on their respective readers, but you also have 3 reprojectors to the same coordinate system in the workflow.
If the source info is not in UTM83-10 then you need to remove the setting on the readers, if it is, then the reprojectors are useless. The 3rd is entirely unneccesary regardless, especially since you explicitly set the projection on the writer as well.
You don't need the RasterSelecto to select all the bands, since you've done nothing upstream to change it from the default.
Is there a NoDataValue (ex 255) on the original ecw? If so you probably want to deal with that before the RasterExpressionEvaluator.
A RasterBandNoDataSetter followed immediately by the NoDataRemover does nothing. Are you sure you don't want the NoDateRemover after the mosaicker?
The main issue is probably with your clipper. Since you tiled your mosaic, it's likely that most of the tiles are entirely inside the clipper, whereas you only have a connection to the ClippedInside port. Note the clipper is Version 5 whereas the latest version is 10, and the ports have changed between versions.
The counter/tester combo also seems entirely unnecessary.
Apart from unnescesay reprojecting and rasterbandselections etc. i would not mosaick the tiles. (takes time and increases subsequent clipping procestime.)
Use a RasterextentCoercer and filter these with the clipper feature. Then Use clipper only on those that pass the filter.
The extents coercer is pretty fast. I just did 138 tiles in 20.5 sec on a quadcore 16Gb mem.
You're going to always have the black bits around the edge with ECWs in FME because v2 doesn't support transparency. FME doesn't write/read v3, but you can work around it if you have software that will.