$var1 = 'abc~123~def';
print join("\n",split(/\~/,$var1))."\n";
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After just throwing at you, I'll try to explain it a little bit. First, I'll write it with some newlines:

1 print
2  join(
3   "\n",
4   split(
5    /\~/,
6    $var1
7   )
8  ).
9 "\n";
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Now let's discuss the lines. I'll take them from inside to outside because it should make the things a little bit easier to understand:
split (4) takes a string (6) and returns an array. Each element of the array is a part of the string without the given seperator (5) which must be given as a regular expression. So you could write this part as:

@MyArray = split(/\~/,$var1);
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The regular expression in this case has / as start and end chars and an escaped ~.
Everything is seperated now, but you also asked to print every part on a line of it's own, so we need to merge our array back to a string where every part is seperated by newlines. join (2) is perfect for this. It takes the first argument, here we have a newline (3), and puts it between every following argument returning everything as a string. Here, the following arguments are taken from the array returned by split (4). Finally, print (1) shows the result to you.

While writing this, I got a really cool idea which would fit your request but I don't think it will fit your problem. Just to be complete, here ist another solution:

$var1 = 'abc~123~def';
$var1 =~ s/\~/\n/g;
print "$var1\n";
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; This one replaces every ~ with a \n using a regular expression:

=~ starts the expression

s means "replace", without it, the expression would only do a match

/ is the start char of the expression

\~ is the seperator char (escaped by \)

/ is the end char for the match part and the start char for the replacement part

\n is a newline, the thing witch should be put in place of the match part

/ is the end char

finally g means "replace all"