To Throw Away
transitive verb, ichidan verb
You throw and throw away something. That's why this means to throw away.
なげすてる
The reading comes from 投げる and 捨てる, combined into one garbage inducing dump of a word.
今朝、六時に目覚ましがなった時に、その時計を投げ捨ててしまいました。
I threw my alarm clock away when it went off at six this morning.