PlotRangeClipping not working correctly with small ImageSize and PDF-export

The reason why this overhang appears is that the Thickness of the line marking the edge of the Disk is not counted as something that needs to be clipped (although it should). The line itself (the center of the thick red line) is clipped correctly.

But of course the result looks very clumsy, and it can only be eliminated if the line thickness is made as small as the thickness of the Frame. So in order to get a prettier result, you have to mask the overhanging line thickness manually. Here is how you could do it:

p1 = Graphics[{EdgeForm[{Red, Thickness[.1]}], FaceForm[], Disk[]}, 
   Frame -> True, PlotRange -> {{0, 1}, {0, 1}}];

Show[p1, With[{d = .2},
  Graphics[
   {White, FilledCurve[
     {
      {Line[{{-d, -d}, {-d, 1 + d}, {1 + d, 1 + d}, {1 + d, -d}}]},
      {Line[{{0, 0}, {0, 1}, {1, 1}, {1, 0}}]}
      }
     ]}
   ]
  ], ImageSize -> 6 cm]

The FilledCurve is a square with a hole in it, like a picture frame with a with border of thickness d = .2 in plot units.

The exported PDF looks like this:

Edit to make it work independently of PlotRange

To make the cropping frame resize automatically with the PlotRange, I went back to the question Changing the background color of a framed plot and saw that there was an answer by István Zachar that also uses FilledCurve and applies Scaled and ImageScaled to the rectangle borders. Using that approach directly still lets some of the red arc peek through in the notebook display, so I combined that approach with my above choice of an extra width d, and that should work for arbitrary PlotRange:

Show[p1, With[{d = .2}, 
  Graphics[{White, 
    FilledCurve[{{Line[
        ImageScaled /@ {{-d, -d}, {-d, 1 + d}, {1 + d, 
           1 + d}, {1 + d, -d}}]}, {Line[
        Scaled /@ {{0, 0}, {0, 1}, {1, 1}, {1, 0}}]}}]}]], 
 ImageSize -> 6 cm]

For more games that you can play with FilledCurve, see e.g. Filling a polygon with a pattern of insets.

Here are the steps to the obtain the PDF's files you want without the problems you showed. I am going by the assumption that there is no simple Plot option we are overlooking here, so this solution uses Inskscape to get the pdf file without the clipping you show.

1) Download the install free software Inskscape

2) Export the images you want to svg and not to pdf

SetDirectory[NotebookDirectory[]]
Export["p2.svg", p2]
Export["p1.svg", p1]

3) Open Inskscape and read p1.svg , then do save as and select PDF and make sure to use the "export area is drawing option"

4) Now open the p1.pdf, and it will be OK

Do the same for p2.pdf :

I've put the pdf files p1.pdf and p2.pdf here for you to check.