The state machine, recursive processing of parenthetic expressions, or similar suggestions of others are more general and, IMO, likely to be more robust solutions. One cannot speak to the issue of speed without more info.

However, I notice in the example you give a characteristic that might be exploited to advantage. Each highest-level parenthetic expression, whatever the nesting within it, is preceded by an alphanumeric ( \w) character and followed by a  '->' sequence allowing the following, perhaps rather fragile, approach:

>perl -wMstrict -le
"my $s = 'TestVar(Test1->(xy))->Var2(Test2(10)(12))->Finalvar';
 $s =~ s{ (?<= \w) \( .+? \) (?= ->) }{}xmsg;
 print qq{'$s'};
"
'TestVar->Var2->Finalvar'
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