How can we neglect copper losses in open circuit test then neglect core losses in short circuit test of transformer?
In an open circuit test, the current flowing in the secondary is zero hence copper loss is zero in the secondary. In the primary, the only current is the magnetization current and, it is this current that causes core saturation. It's usually a small fraction of full load primary current hence, those copper losses associated with core saturation current are quite small and can be ignored.
In a short circuit test, the applied voltage on the primary is very much smaller than that applied in proper applications hence, the magnetization current is very much smaller and, because of this, core losses are fairly negligible. Copper losses dominate short circuit testing because the applied voltage to the primary is chosen to produce the equivalent of full-load currents.