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I opened a raster file as a layer, and click the right mouse button and select "Save as..." to change the resolution. I got the new raster, but I want to know what is the method (average, aggregation...) of this mode?

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Save as... is based on gdal_translate https://www.gdal.org/gdal_translate.html and gdaladdo https://www.gdal.org/gdaladdo.html for the image pyramids. By the documentation of gdal_translate the default method is nearest.

-r {nearest (default),bilinear,cubic,cubicspline,lanczos,average,mode}: (GDAL >= 2.0) Select a resampling algorithm.

I do not see a sign about using some other resampling method than the default in QGIS source code

It might be worth making a feature request about about adding a control that allows user to select the resampling method.

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