As discussed in a previous installment, the water with one washed Netilat Yadayim in the morning is considered impure, and could cause harm to those who step on in. Therefore, one must ensure not to wash his hands in a place where people walk, and to wash instead directly into a sink, or into a utensil and then pour the water down a drain.
If one mistakenly washed Netilat Yadayim on the ground in a place where it could be stepped on, he must pour more water over it to wash it away, out of concern for the wellbeing of others. The Poskim address the question of how much water is needed to wash away the contaminated water. The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) writes that one should pour "a lot of water," without specifying a particular quantity. The Yalkut Yosef writes that the Halacha in this case might resemble the Halacha requiring pouring a Rebi'it of water over urine to eliminate its status as urine so that one may read the Shema in its presence (Shulhan Aruch, Orah Haim 77:1). Perhaps the same small amount is required to eliminate the impurity of water that had been used for Netilat Yadayim. On the other hand, the Yalkut Yosef adds, one could argue that more water is needed in the case of water used for hand-washing. Hacham Ovadia Yosef, in Yabia Omer (vol. 3, 1:9), brings different views regarding this question. Hacham Avraham Hamwey (Aleppo, 1838-1886) shows that according to the Hida (Rav Haim Yosef David Azulai, 1724-1806), water used for hand-washing has a stricter status than that of urine, and thus a large amount of water is needed to eliminate this status. Many others, however, as Hacham Ovadia cites, ruled leniently, that it suffices to pour just a Rebi'it of water over the water used for washing. Hacham Ovadia appears to favor the lenient position. By contrast, Rav Ovadia Hedaya (1889-1969), in Yaskil Abdi, rules that one must use more water than the amount of contaminated water. It is preferable to follow this stringent opinion.
The Yalkut Yosef writes that if the water used for Netilat Yadayim spilled over a tiled floor, it may be cleaned with a mop or rag. At first glance, one might question this ruling, in light of the fact that the water will contaminate the mop or rag which absorbs it. Rav Yisrael Bitan suggests explaining this ruling in light of a teaching of the Ben Ish Hai concerning the handles of the cup used for Netilat Yadayim. In his Od Yosef Hai, the Ben Ish Hai writes that one may hold the handles of the cup as he pours the water over his hands, even though there are contaminated droplets of water on the handles from when he first touched them. The reason, the Ben Ish Hai explains, is that the harmful spiritual forces are "arrogant" and only bother affecting significant water. The droplets on the handles, which are hardly visible, are regarded as "beneath their honor," and so they do not bother affecting it. It stands to reason that this applies also to water absorbed by rags or a mop, and so the water that had been used for washing may be cleaned with a rag or mop.
Summary: If one mistakenly washed Netilat Yadayim in the morning in a place where people might step on them, or if the water spilled in such a place, he must pour water over them so they are not stepped on. Preferably, he should pour an amount of water exceeding the amount of contaminated water on the ground. If the water spilled on a tiled floor, it may be cleaned with a rag or mop.