Sheikh M. S. Al-Munajjid, a prominent Saudi Muslim lecturer and author, states:

The Muslim scholars agree that there is nothing wrong with using siwak (teeth-brush) during the day when one is fasting, but they differed with regard to using it afternoon, which some of them see as disliked (makruh).
The correct view is that it is Sunnah for one who is fasting, just as it is for anyone else, because of the general sense of the reports which prove that it is Sunnah. The Prophet (peace and blessings be upon him) did not make any exceptions or state any specific time, and a statement that is general in nature should be construed as denoting a general implication unless there is evidence to indicate that it is specific in application.
the hadith quoted as evidence to forbid using siwak afternoon is attributed to `Ali ibn Abi Talib (may Allah be pleased with him) who quoted the Prophet (peace and blessings be upon him) as saying, “When you fast, use siwak in the morning but do not use it in the afternoon.” (Reported by al-Daraqutni) This is a da`if (weak) hadith. There is no proof that this can be attributed to the Prophet (peace and blessings be upon him).
With regard to the use of the hadith: “The odor that comes from the mouth of the fasting person is better in the sight of Allah than the scent of musk” (Reported by Al-Bukhari and Muslim) as evidence, this mouth odor will not be dispelled by use of siwak because it is caused by having empty stomach, and this could occur early in the day if a person has not eaten suhur.
all the scholars agree that it is permissible for a fasting person to use siwak early in the day. This shows that use of siwak is encouraged even when fasting, and there is no difference between using it early in the day or later on.

Sheikh `Atiyyah Saqr, former head of Al-Azhar Fatwa Committee, adds:

The view I believe to be most correct regarding the use of siwak during the day of fasting is that it is not blameworthy to clean one’s teeth by any means, provided that no toothpaste, blood or things of the sort reaches the stomach. However, in order to be cautious, it is better to clean one’s teeth at night before fasting.