Avraham himself objected — the text is explicit that this was G-d’s decision, not his.
Q. How could Abraham dismiss Hagar and Yishmael in such a way?
Your question is on G-d, not on Abraham- for it was Abr. who did not (!) want to chase away Hagar and Yishmael (Gen. 21, “and it was very (!) bad in the eyes of Abr.”), but G-d nevertheless told him to do so, as He explains there explicitly, so that it should be clear to all (and forever!) that Isaac, and not Yishmael, is the sole continuation of the Chosen Nation. Additionally, although the Torah is usually very concise when it comes to giving insignificant details, G-d does (!) feel it significant to write explicitly that Abr. himself (not through his servants) made sure to give them food and water (see there), and apparently she was heading back to her father’s family (as was the custom for divorced women). The Torah infers that their provisions were enough, but the problem is that they got lost and wandered [21, 14-15, the Hebrew word “vateta”, is translated in the classic translations and commentaries (Unkolos and Targ. Yonatan, Rashbam, Ibn Ezra, etc.): “and got lost”] and only consequently of their getting lost, they ran out of water. This is also clear from the use of this root, in other places that it’s always “to leave the path” (Psalms 119, 110; Ezek, 14, 11), or in our context, to get lost. It should also be pointed out that Hagar knew her way back to Egypt (see Gen. 16, 6 and on), but somehow here, she got lost.
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