Removing voltage spikes and overshoots using power MOSFET as switch and 555 timer as pulse generator
1. Improve your MOSFET layout (edited)
First remove any resistance or use a small current shunt (less than 0,1 Ohm) between the source of the MOSFET and the ground. A N-MOSFET is controlled by the voltage between gate and source Vgs. The LM555 output is referenced to the ground, so must be the source of your MOSFET.
2. Take care of the LM555
Then add a small resistor between the LM555 output and the gate. The LM555 seems to be able to source only 200mA (according to datasheet http://www.ti.com/lit/ds/symlink/lm555.pdf), so according to the voltage you use and inner gate resistor of your N-MOSFET, check that you are not trying to drive to much current from the LM555. This can be the explanation of the voltage drop when connecting the MOSFET.
3. Control the LED current (edited)
Finally, if you are trying to drive a power LED, you should consider to drive it with a current source. Power LED must be current-controlled as forward voltage is dependent of LED temperature and current flowing through the LED. Take a look of page 2 and 7 of your datasheet. Variation are about 10% for both. So if you apply a constant voltage to the LED you will get a various luminosity as the LED gets warm.