I wouldn't use splice at all. Instead I'd merge the two arrays:

#!/usr/bin/perl
use strict;
use warnings;


my @first  = qw(Can unlock secret);
my @second = qw(you the code?);
my @interleave;

push @interleave, grep {$_} (shift @first), shift @second
    while @first || @second;

print "@interleave";
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Although you could use splice to do an "in place' merge:

#!/usr/bin/perl
use strict;
use warnings;

my @first  = qw(Can unlock secret);
my @second = qw(you the code?);

splice @first, @second, 0, pop @second while @second;

print "@first";
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or avoiding destroying the contents of @second:

...
splice @first, $_, 0, $second[$_ - 1] for reverse 1 .. @second;

print "@first";
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or using splice to populate a new array:

my @new;

splice @new, 0, 0, $first[$_], $second[$_] for reverse 0 .. $#second;
print "@new";
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Note that a few of these do stuff backwards to avoid having to account for elements that have been inserted into the target array.

Now, to answer your actual question. First lets add diagnostics a little differently to your existing code:

#!/usr/bin/perl
use strict;
use warnings;


my @first = qw(Can unlock secret);
my @second = qw(you the code?);

dumpArrays('start', \@first, \@second);

splice(@first, 1, 0, @second[0,-2]);
dumpArrays('first', \@first, \@second);

my @newArray = @first;

splice(@newArray, 5,0,@second[0,2]);
dumpArrays('na', \@first, \@second, \@newArray);

my @newArray1 = @newArray;

splice(@newArray1, 2,1);
dumpArrays('na1', \@first, \@second, \@newArray1);

my @newArray2 = @newArray1;

splice(@newArray2, 4,1);
dumpArrays('na2', \@first, \@second, \@newArray2);

my @newArray3 = @newArray2;

splice(@newArray3,3,0, @second[1,1]);
dumpArrays('na3', \@first, \@second, \@newArray3);


sub dumpArrays {
    my ($msg, @arrays) = @_;

    printf "%-10s %s\n", $msg, join '|', map {"@$_"} @arrays;
}
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Prints:

start      Can unlock secret|you the code?
first      Can you the unlock secret|you the code?
na         Can you the unlock secret|you the code?|Can you the unlock 
+secret you code?
na1        Can you the unlock secret|you the code?|Can you unlock secr
+et you code?
na2        Can you the unlock secret|you the code?|Can you unlock secr
+et code?
na3        Can you the unlock secret|you the code?|Can you unlock the 
+the secret code?
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Note that the error doesn't happen until the very last step. In that step you splice(@newArray3,3,0, @second[1,1]);. @second[1,1] which inserts two copies of the word 'the'. You just needed $second[1] there.