I haven't seen a completely substr() solution yet, so here's one:

#!/usr/bin/perl
my $str = "cat"; 
for (reverse 0..(length($str)-1)) { substr($str,$_,1) x= rand(9)+1; }
print "$str\n";
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Random stuff that occurs to me:

• I think this is the first time I've ever used the x= operator
• I assumed (as everyone else) that you want at least 1 of each letter (i.e., that you don't want to delete letters)
• I hope it's clear why the reverse is necessary