For the Stack Overflow rules lawyers; I know this isn't a complete answer, but its too long for a comment.
As a non-speaker of the language, its rather difficult for me to identify differences here. There's quite a lot of text, and while I can see that the fonts are different, its not clear to me that the individual glyphs are. Can you point to one specific glyph there that is incorrect after it is copied ?
The font embedded in the file (Arial Unicode MS) has an attached ToUnicode CMap which looks correct to me, however several of the single character codes map to multiple Unicode code points. Eg character code 0x564 maps to the Unicode values 0x093e, 0x0901.
I have no way to tell easily if this is correct. I could laboriously decode the entire string, check to see what the Unicode code points are and then try and match those to the characters in the original file by placing them individually in a Word document, using Arial Unicode MS. But it looks to me like an awful lot of the characters are correct, and I don't want to waste a lot of time doing that.
[edit]
So this is what the text in the PDF file looks like. The character code is the actual character code in the PDF file, that maps to a glyph program in the font via the CMap and other parts of the font machinery that we needn't worry about here. It also maps via the ToUnicode CMap to a set of Unicode code points
code Unicode glyph name
059A 0938 स Sa
0565 0902 ं vowel sign Anusvara
0597 093F ि vowel sign I
05A8 0948 ै vowel sign Ai
0589 0927 ध Dha
059E 093E ा vowel sign Aa
059F 0935 व Va
058A 0928 न Na
0577 0915 क Ka
Doing my best to recall how to read Devanagri, I believe the original is something like Sa (with 'am' diacritic) Va (with the ai vowel modifier) Dha (with the Aa vowel modifier) Na (with the i vowel modifier) and finally Ka.
I'm afraid that the reason this doesn't cut and paste properly is simply because the ToUnicode values seem to be partially incorrect. The character code 0x0597 has been assigned the Unicode value U+093F when it should be U+0935 and the character code 0x059f has been assigned the Unicode code point U+0935 when it should be U+093F. That is the Unicode values of those two character codes have been transposed.
When you copy and paste this you end up with incompatible modifiers, which is why you get the funny characters. The dashed ring in the glyph indicates where the character being modified by the accent should be. You should never see this, but because the layout engine can't find a base character to modify it just draws the accent on its own.
I'm afraid that your PDF file has been badly made, the only way to fix this would be to correct the errors in the ToUnicode CMap. I did do this for the two characters I noted above, and this then copies and pastes as :
संवैधाषनक
Which looks more or less correct (I seem to have made an error with one vowel modifier). However there may be other faults in that table, and its very much non-trivial to try and correct it. Its taken me the best part of a couple of hours to work out that problem, verifying the entire CMap would take me a day or two. And that CMap is particular to this document, I couldn't use it elsewhere because the font is a subset. A different document would have a different subset, which would mean the character codes would be different.