Physical disability, in general, does not affect a person's obligation to keep mitzvot. Someone who must use a wheelchair, for example, is obligated in all 613 mitzvot. However, there are three kinds of disability regarding which the sources suggest that a person was not obligated in mitzvot at all.
The first category is the "shoteh" - an "insane" or otherwise mentally impaired individual who is unable to comprehend the concept of Divine commandment or understand the actions he must perform. Such a person cannot be said to be "commanded", since no command was ever made to him in a way he could understand.
The second category is the "heresh", or mute person, who is mentioned alongside the "shoteh" and children as people not obligated in mitzvot. This equation is hard to understand nowadays, but once it made sense. Typically, a person was mute as a consequence of being deaf. The deaf could not learn anything from others except by reading, and reading materials were rare before the printing press was invented. Similarly, there were no speech therapists, no sign language, and no teaching of lip reading. So deaf people, too, was not "commanded", since they had no way of hearing Divine commands. (The Biblical idiom for to "obey" is to "listen to the voice of". The deaf literally could not "listen to the voice".) Nowadays, when we do have effective ways of communicating with and teaching the deaf, I believe halachic authorities generally view the deaf as having equal obligations to hearing Jews.
The third category is the blind. According to the accepted opinion, blind Jews have exactly the same halachic obligations as everyone else (except for a few mitzvot which explicitly involve seeing). However, there are minority opinions which suggest that this might not be the case. The most interesting opinion is that of the Pri Megadim (intro to Orach Chaim part 3), who holds that according to one opinion in the gemara, the blind are obligated in negative mitzvot, but not positive mitzvot.
What is the logic behind this distinction? One possibility (see here) is that the blind do not really need to do mitzvot, but they do need to be distinguishably Jewish. And violating a negative mitzvah does more to show that one is not Jewish: if I see you eat pork then I know you violate halacha, but if I do not see you praying it is possible that you will pray at some other time in the day.
The difficulty with this understanding is that it assumes the blind are like the deaf and insane - people to whom the concept of mitzvot cannot apply, since they do not have mental capacity. But a blind person does have mental capability, can communicate normally with other people, and can learn all of the Oral Torah at the very least. So it seems easier to me to say that the blind are inherently commanded and obligated in mitzvot but exempted from some, rather than that they are inherently exempt but have a special obligation in some.
Thus I want to explain as follows. Blind people have no limitations to their mental ability. Thus, they should be obligated in mitzvot. But they do have significant limitation on their actions. For example, wherever they go they are liable to stumble on things and injure themselves. And they have difficulty locating objects in order to perform actions using those objects.
Another class of people - women - also has limitations on the set of mitzvot they must do. At certain times, due to pregnancy and raising children, women are busy and unable to spend time on other commitments. Thus, women are exempt from positive time-related mitzvot. I suggest that since blind people face larger and more constant restrictions on their actions than do women, they have a larger mitzvah exemption. Rather than being exempt from positive time-related mitzvot, perhap they should be exempt from all positive mitzvot. Meanwhile, the limitations on blind people's actions do not impair their ability to uphold negative mitzvot, since by sitting and doing nothing they do not violate any negative mitzvah. Thus, they should be obligated in negative but not positive mitzvot. That is the exact combination which the Pri Megadim suggests.