In the realm of regular synchronic processes, vowel dissimilation is relatively uncommon (dissimilation itself is uncommon, and vowel-to-vowel dissimilation is most uncommon); however, it does exist. Examples are low-vowel dissimilation in Woleaian where /a/ becomes [e] before a in the next syllable (described in Sohn 1971), and reportedly the rule is found in Marshallese. Kera dissimilates /a/ to [ə] (or [ɨ]: sources differ). Wintu has a dissimilation where /e,o/ become [i,u] before /a/, though only lexically specified root vowels undergo this dissimilation. Finally, a fairly well-knownish (but under-documented) example of this type are dissimilative akan'e and jakan'e in SW Russian and NE Belorussian dialects: see Nesset 2002 for data and analysis.
One example of backness dissimilation is reported (Ito 1986). There is a stem-formation process in Ainu where various vowels may be added; within the subset where a high vowel is selected, the suffix is back after front vowels and front after front vowels. It is interesting that raising of low vowels is virtually the only kind of V-to-V dissimilation attested (lowering of high vowels, for example, is unknown).
There is a straightforward explanation for why harmony and disharmony are so different in their "totality". In the case of harmony, it is typically said that vowels must be the same for the spreading feature, so all vowels must be [+ATR] if one is. That is cashed out as a local requirement that a vowel must be [+ATR] if it is adjacent to a [+ATR] vowel – this iterates through the word, effecting complete spread of [+ATR] to all vowels (because each time the rule applies, a new environment is created). In the case of dissimilation, each time the rule applies, the environment is destroyed: so /pataka/ → [pateka], with no two adjacent low vowels. Hence dissimilations almost always create an alternating pattern, and you don't find a situation where "there can be only one low vowel in a word".