There is nothing in the .NET framework that will help you with this out-of-the-box.
The most common spelling mistakes are those where the letters are a decent phonetic representation of the word, but not the correct spelling of the word.
For example, it could be argued that the words sword
and sord
(yes, that's a word) have the same phonetic roots (they sound the same when you pronounce them).
That being said, there are a number of algorithms that you can use to translate words (even mispelled ones) into phonetic variants.
The first is Soundex. It's fairly simple to implement and there are a fair number of .NET implementations of this algorithm. It's rather simple, but it gives you real values you can compare to each other.
Another is Metaphone. While I can't find a native .NET implementation of Metaphone, the link provided has links to a number of other implementations which could be converted. The easiest to convert would probably be the Java implementation of the Metaphone algorithm.
It should be noted that the Metaphone algorithm has gone through revisions. There is Double Metaphone (which has a .NET implementation) and Metaphone 3. Metaphone 3 is a commercial application, but has a 98% accuracy rate compared to an 89% accuracy rate for the Double Metaphone algorithm when run against a database of common English words. Depending on your need, you might want to look for (in the case of Double Metaphone) or purchase (in the case of Metaphone 3) the source for the algorithm and convert or access it through the P/Invoke layer (there are C++ implementations abound).
Metaphone and Soundex differ in the sense that Soundex produces fixed length numeric keys, whereas Metaphone produces keys of different length, so the results will be different. In the end, both will do the same kind of comparison for you, you just have to find out which suits your needs the best, given your requirements and resources (and intolerance levels for the spelling mistakes, of course).