You need to be more selective about what you are matching, and will have to repeat the substitution until all nested matches are removed

use strict;
use warnings;
my $string="TestVar(Test1->(xy))->Var2(Test2(10)(12))->Finalvar"; 
while ($string=~s/   # repeat while we make matches
\(                   #beginning of a parenthesised group
[^)(]+               # non parentheses charaters 
\)                   # end of group
//gx)
{}
print "$string\n";
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This will remove parenthesised groups, starting from the innermost

Edit: tidied up comments in code block