Since this is a formal statement, it's better to keep 私の. But people can understand the sentence without it because they know it's your profile.
What's worse about your sentence is that your sentence has a number of bad word choices and grammatical errors.
- 生むています is always ungrammatical. The te-form of 生む is 生んで.
- There is a subject-predicate mismatch. 私の目的は生んでいます is "My mission is (in the process of) producing something" rather than "My mission is to produce something". You have to nominalize 生む.
- 主導 refers to an act of leading, but it does not refer to an ability to take a lead role.
- 代表的な執行 sounds like "representative execution" rather than "outstanding performance".
- 例外的な does not have a positive connotation like that of "exceptional". 例外的な質 sounds like "peculiar quality" rather than "exceptional value".
- 通じて needs a particle を.
- (EDIT) This is a relatively minor problem, but consider using 目標 instead of 目的. The former refers to a long-term mission/goal, whereas the latter is closer to "purpose".
A corrected version is something like:
Or if you don't like katakana loanwords, an alternative free translation would be: