The first problem here is that you haven't asked a question! Perhaps ...

you don't understand why you're getting the output you see (which you don't show)

you want to know how to get the expected output (which you don't specify)

you don't understand some part of the documentation

you want a different way to do it
Please read the guidelines in: How do I post a question effectively?
The code you've provided outputs:
1
Statistics::Descriptive::Sparse=HASH(0x7fa3510457f0)
Presumably you want:
1
0
Checking the documentation for Statistics::Descriptive, you can achieve this by changing
my $min_index = Statistics::Descriptive::Sparse>new();
$min_index > mindex(@array1);
to
my $stat = Statistics::Descriptive::Sparse>new();
$stat>add_data(@array1);
my $min_index = $stat>mindex();
See also ++Khen1950fx's response (above) which has similar code changes.
I see a number of alternative ways of doing this (without using Statistics::Descriptive) have already been provided. Here's another one that doesn't use any modules at all and handles nonunique values and arrays of uneven lengths.
#!/usr/bin/env perl
use strict;
use warnings;
my @data = (
[ [ 1 .. 7 ], [ qw{a b c d e f g} ] ],
[ [ 1 .. 7, 0 ], [ qw{a b c d e f g} ] ],
[ [ 1 .. 7, 0 ], [ qw{a b c d e f g h} ] ],
[ [ 1 .. 7, 1, 0 ], [ qw{a b c d e f g h} ] ],
[ [ 1 .. 7, 1 .. 7 ], [ qw{a b c d e f g} ] ],
);
for (@data) {
my @array1 = @{$_>[0]};
my @array2 = @{$_>[1]};
my $pos = 1;
my $min_pos = (
sort { $a>[0] <=> $b>[0] } map { [$_ => ++$pos] } @array1
)[0];
print "Array1: @array1\n";
print "Min value: $min_pos>[0]\n";
print "Min index: $min_pos>[1]\n";
print "Array2: @array2\n";
if ($min_pos>[1] > $#array2) {
print "Min index outside \@array2 bounds!\n";
}
else {
print 'Min index position in @array2 has value: ',
"$array2[$min_pos>[1]]\n";
}
print '' x 60, "\n";
}
Output:
$ pm_min_mindex.pl
Array1: 1 2 3 4 5 6 7
Min value: 1
Min index: 0
Array2: a b c d e f g
Min index position in @array2 has value: a

Array1: 1 2 3 4 5 6 7 0
Min value: 0
Min index: 7
Array2: a b c d e f g
Min index outside @array2 bounds!

Array1: 1 2 3 4 5 6 7 0
Min value: 0
Min index: 7
Array2: a b c d e f g h
Min index position in @array2 has value: h

Array1: 1 2 3 4 5 6 7 1 0
Min value: 1
Min index: 7
Array2: a b c d e f g h
Min index position in @array2 has value: h

Array1: 1 2 3 4 5 6 7 1 2 3 4 5 6 7
Min value: 1
Min index: 0
Array2: a b c d e f g
Min index position in @array2 has value: a

You may find Benchmark useful for comparing the alternative solutions supplied.