Code
%%// Input data and params
a = imread('Lenna.png');
a = rgb2gray(a);
src_xy = [300,300]; %% Starting X-Y of the source from where the portion would be cut from
src_dims = [100 100]; %% Dimensions of the portion to be cut
tgt_xy = [200,200]; %% Starting X-Y of the target to where the portion would be put into
%%// Get masks
msrc = false(size(a));
msrc(src_xy(1):src_xy(1)+src_dims(1)-1,src_xy(2):src_xy(2)+src_dims(2)-1)=true;
mtgt = false(size(a));
mtgt(tgt_xy(1):tgt_xy(1)+src_dims(1)-1,tgt_xy(2):tgt_xy(2)+src_dims(2)-1)=true;
%%// If you would like to have a cursor based cut, explore ROIPOLY, GINPUT - e.g. - mask1 = roipoly(a)
mask1 = msrc;
a2 = double(a);
%%// Get crop-mask boundary and dilate it a bit to show it as the "frame" on the original image
a2(imdilate(edge(mask1,'sobel'),strel('disk',2))) = 0;
a2 = uint8(a2);
%%// Display original image with cropped portion being highlighted
figure,imshow(a2);title('Cropped portion highlighted')
figure,imshow(a);title('Original Image')
figure,imshow(mask1);title('Mask that was cropped')
img1 = uint8(bsxfun(@times,double(a),mask1));
figure,imshow(img1);title('Masked portion of image')
%%// Get and display original image with cropped portion being overlayed at the target coordinates
a_final = a;
a_final(mtgt) = a(msrc);
figure,imshow(uint8(a_final));title('Original image with the cut portion being overlayed')
Output
Please note that to use RGB images, you would need to tinker a bit more with the above code.