A tile or masonry saw assembly comprising: - a saw device including a motor arranged to run a saw blade to cut a workpiece in a cutting direction; - a frame that is arranged to support the saw device such that it is enabled to move relative to the frame to execute cutting operations by means of the saw blade; - a workpiece support operably coupled to the frame to support the workpiece relative to the saw device, and to allow the workpiece support to be moved along the frame; and - a cover assembly that has a first longitudinal extension and in turn comprises a cover and a supporting structure, and has a front end that is arranged to face the saw blade and a rear end that is arranged to face away from the saw blade, where the cover assembly comprises a dust hose attachment that is positioned at the rear end and is arranged to be connected to a vacuum dust collection arrangement; characterized in that said cover assembly is releasably attachable to the workpiece support, where the supporting structure comprises a base that is arranged to be attached to the workpiece support; and in that the workpiece support has a second longitudinal extension (L w), where furthermore the base is arranged to be attached to the workpiece support by means of co-operating fastening means comprised in both the base and the workpiece support, where these fastening means are intended to engage each other such that the base and the workpiece support both extend straight such that the first longitudinal extension runs parallel to the second longitudinal extension (L w) when the base is attached to the workpiece support, where the cover is movable relative to the base in the first longitudinal extension, - a saw device including a motor arranged to run a saw blade to cut a workpiece in a cutting direction; - a frame that is arranged to support the saw device such that it is enabled to move relative to the frame to execute cutting operations by means of the saw blade; - a workpiece support operably coupled to the frame to support the workpiece relative to the saw device, and to allow the workpiece support to be moved along the frame; and - a cover assembly that has a first longitudinal extension and in turn comprises a cover and a supporting structure, and has a front end that is arranged to face the saw blade and a rear end that is arranged to face away from the saw blade, where the cover assembly comprises a dust hose attachment that is positioned at the rear end and is arranged to be connected to a vacuum dust collection arrangement; characterized in that said cover assembly is releasably attachable to the workpiece support, where the supporting structure comprises a base that is arranged to be attached to the workpiece support; and in that the workpiece support has a second longitudinal extension (L w), where furthermore the base is arranged to be attached to the workpiece support by means of co-operating fastening means comprised in both the base and the workpiece support, where these fastening means are intended to engage each other such that the base and the workpiece support both extend straight such that the first longitudinal extension runs parallel to the second longitudinal extension (L w) when the base is attached to the workpiece support, where the cover is movable relative to the base in the first longitudinal extension,