This is a lyric from "Achilles Come Down" by Gang of Youths. Is "absent of cause" proper grammar or a stylistic form?
It is a rather obscure expression (absent of + noun) but Ngram does find incidences of this use, which seems to be more popular around the beginning of the 1800s.
Hardly any dictionary includes this use, I could only find:
While the giant has made efforts recently to elevate quality reporting in its algorithms, most of those ranking decisions are made absent of human judgement. (Dictionary.com)
One can guess that it is used with the meaning of (de)void of... My advice, enjoy it in the song, but avoid using it in other contexts. There are other more idiomatic ways of saying the same.
This is only a supposition, but it may be an adaptation of the use of absent as a preposition:
preposition FORMAL•NORTH AMERICAN
- Absent a willingness to negotiate, you can't have collective bargaining. (OxfordL)