The regex option m here does not do what you think. First, it's not required to match/replace multiple newlines in a string.  Secondly, it has no influence on the behavior of the readline (<>) in the implicit while loop behind the command line option -p. In other words, all you ever have in $_ is one line of text...

One way around the problem would be to set the input record separator to undef to slurp in the whole file at once

$ printf "Line1\nLine2\nLine3\n\nXYZ: Blah\n" | perl -p -e "$/=undef; 
+s|\nXYZ.+\n||"
Line1
Line2
Line3
[download]

(You can also say BEGIN { $/=undef } ... if you want to have it execute only once at the expense of a few more keystrokes.)

Whether that is a good solution depends on the circumstances, e.g. how large the input file is, etc.  In case it's huge, you might want to read it in single line mode, and have previous lines accumulate in a buffer up until the search pattern is found. In this case, you can trim the trailing newline in the buffer before printing it out.

$ printf "Line1\nLine2\nLine3\n\nXYZ: Blah\n" | perl -n -e '$buf.=$_; 
+if ($buf=~s|\nXYZ.+\n||) {print $buf; $buf=""}'
Line1
Line2
Line3
[download]