Of course, there is such a word as irregardless!
In fact, it is a century-old colloquial word that means the same as irrespective and regardless, and it may have come about by some fusion or confusion of those two words. The use of irregardless is a common peeve among people who question illogical new words and phrases in English, but the word is not as bad as many people think. No English speaker who hears the word irregardless actually interprets it as meaning not without regard. We might find the word annoying, but we know exactly what the speaker means. And though irrespective and regardless have perhaps lost some ground since the arrival of irregardless, they are still widely used, and they prevail over irregardless by a large margin in edited publications.