Use 4 arg substr:

$ time perl -e '$a = "a" x 50_000; substr($a, 0, 1, "") while length($
+a);'
real    0m0.016s
user    0m0.012s
sys    0m0.008s
ysth@cat:~$ time perl -e '$a = "a" x 100_000; substr($a, 0, 1, "") whi
+le length($a);'
real    0m0.029s
user    0m0.024s
sys    0m0.004s
ysth@cat:~$ time perl -e '$a = "a" x 200_000; substr($a, 0, 1, "") whi
+le length($a);'
real    0m0.041s
user    0m0.036s
sys    0m0.004s
[download]

Or even s/.//s; Either will trigger an optimization that just adjusts the effective start of the string buffer without moving the data at all (when removing characters from the start of the string).