I can see the ch mutates to g, but not sure why there is a ch and c form - is this just a north/south difference?
The base form of the word is "clywed". "C" can mutate in three ways, softly to a "g", nasaly to "Ngh" and aspirately to "ch". Sometimes whilst it may technically possible for a word beginning with "C" to mutate in these three ways it might simply never actually happen or happens rarely. As it happens there are fairly common circumstances in which "clywed" could mutate in these three ways. 1-softly in a phrase like "Ceisiais i i glywed" (I tried to hear). 2-nasaly "Mi wnaeth o fy nghlywed i" (He heard me). 3-aspirately "Ni chlywais i'r drws yn cau" (I didn't hear the door close. NOTE: in your comment you said "Ch" mutates to "g", "Ch" does not mutate it is only the product of a "C" to "g" mutation or a word naturally starts with it. (here is a link to a good mutations grid: https://31.media.tumblr.com/tumblr_m9ox8wy0rR1rw84ef.png)