One meaning of the verb, 'to hoy', was to urge on or incite in older times. That came from the fact that the people doing the urging would shout 'Hoy! Hoy!' in much the same way, I imagine, as we might shout 'Go! Go!' today.
I can't quite see the connection with throwing something away, other than the fact that there is a 'moving on' concept involved.
Could be a variation of 'hoick' as in 'hoick it out of the window'. This word belongs to the group that includes 'heave, hike, heist, hoist', etc, implying raising or throwing.
The Dictionary of the Scots Language defines Hoy as TO HEAVE UP (A HEAVY OBJECT) TO THROW OR TOSS UP and says it comes from hoise (meanining hoist) via Low German and Dutch.