You can replace commas with a non-punctuation character, remove all remaining puctuation, then restore the commas:
awk -v local="[ 'service center','New' ]" '
gsub(/,/, SUBSEP, local)
gsub(/[[:punct:]]/, "", local)
gsub(SUBSEP, ",", local)
local=" service center,New "
Here, I'm using the builtin SUBSEP variable, described in the GNU awk manual thusly:
The default value of
SUBSEP is the string
"\034", which contains a nonprinting character that is unlikely to appear in an awk program or in most input data