If I have understood correctly, you could localise the input record separator (see $/ or $INPUT_RECORD_SEPARATOR in perlvar) to your closing tag then use tr to remove embedded newlines.

With this input data

$ cat spw822595.inp
<MyId><data>1332</data><blarg>burfle bof
bip blech</blarg></MyId><MyId><data>1332</data><spu>hsh wugw </spu>
<spog>uh wef wegf</spog></MyId>
<MyId><data>1332</data><grop>hd wg fw we we we we
eryer efy we dad</grop></MyId>
$
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This code

use strict;
use warnings;

my $inFile = q{spw822595.inp};
open my $inFH, q{<}, $inFile
   or die qq{open: < $inFile: $!\n};
my $outFile = q{spw822595.out};
open my $outFH, q{>}, $outFile
   or die qq{open: > $outFile: $!\n};

{
    local $/ = q{</MyId>};
    while ( <$inFH> )
    {
        tr{\n}{}d;
        print $outFH qq{$_\n} if $_;
    }
}

close $inFH
   or die qq{close: $inFile: $!\n};
close $outFH
   or die qq{close: $outFile: $!\n};
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Produces this output

$ cat spw822595.out 
<MyId><data>1332</data><blarg>burfle bofbip blech</blarg></MyId>
<MyId><data>1332</data><spu>hsh wugw </spu><spog>uh wef wegf</spog></M
+yId>
<MyId><data>1332</data><grop>hd wg fw we we we weeryer efy we dad</gro
+p></MyId>
$
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I hope I have understood correctly and this is of use.

Update: Just spotted a horrible typo in first paragraph, s{\$\.}{$/} has put things right :-(