If you have worked in layers in Photoshop then you should have a transparent background. You have several options:
Merge your layers but do not flatten the image
Save As a PSD with a different name and open or place it in your Illustrator workspace. Transparency will be preserved.
Or Save for Web using PNG as the selected format and with Transparency selected. Transparency will be preserved.
Or Save for Web using GIF as the selected format and with Transparency selected. Transparency will be preserved.
Or after merging layers, select the layer and Create a Workpath using the Paths Palette. Export the Path to Illustrator. Open the path in Illustrator and place the image file. Position the paths in position and on top of the image. Select both and execute a mask command.
What do you mean when you say cut and tuned in photoshop? do you mean cleaned off all the excess around the image you are importing to Illustrator? If so, make sure that the layer in photoshop has a transparent background, save as a .psd, open in Illustrator and keep the layers do not flatten the image. That white box is not going to go away without deleting the image since it is a raster image; it comes with a clipping mask around it so if you plan on printing and cutting you need to make a CUT path on the layer above the raster image first.