Just use a recursive routine to drill down. Witness:

my @array=(['john','tom','peter'],['rose','teak'],['car','truck','jeep
+'],['trees','plants'],['good','bad','ugly']);
my @arrayindex=(3,1);

my @wanted = @array[@arrayindex]; # get slice
show(@wanted);
sub show {
  if (ref @_[0]) { # still recursing
    for (@{+shift}) {
      show(@_, $_);
    }
  } else { # end case
    print "@_\n"; # do what you want with the results here
  }
}
[download]

This prints:

trees rose
trees teak
plants rose
plants teak
[download]